Dr. Carleen Eaton continues on to Algebra 2, and brings with her 10 years of experience in teaching math and science. This course meets or exceeds all state standards and is essential to those having trouble with Algebra in high school or college. With her clear explanations and examples of commonly seen problems, Dr. Eaton will make sure you understand all the confusing concepts in Algebra 2, ranging from Quadratic Inequalities to Matrices and Conic Sections. Dr. Carleen Eaton has an M.D. from the UCLA School of Medicine and in her teaching career has won numerous "Teacher of the Year" awards. She is also continually ranked as one of the top instructors in California.
| I. Equations and Inequalities |
| |
Expressions and Formulas |
22:23 |
| | |
Intro |
0:00 | |
| | |
Order of Operations |
0:19 | |
| | |
| Variable |
0:27 | |
| | |
| Algebraic Expression |
0:46 | |
| | |
| Term |
0:57 | |
| | |
| Example: Algebraic Expression |
1:25 | |
| | |
| Evaluate Inside Grouping Symbols |
1:55 | |
| | |
| Evaluate Powers |
2:30 | |
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| Multiply/Divide Left to Right |
2:55 | |
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| Add/Subtract Left to Right |
3:35 | |
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Monomials |
4:40 | |
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| Examples of Monomials |
4:52 | |
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| Constant |
5:27 | |
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| Coefficient |
5:46 | |
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| Degree |
6:25 | |
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| Power |
7:15 | |
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Polynomials |
8:02 | |
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| Examples of Polynomials |
8:24 | |
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| Binomials, Trinomials, Monomials |
8:53 | |
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| Term |
9:21 | |
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| Like Terms |
10:02 | |
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Formulas |
11:00 | |
| | |
| Example: Pythagorean Theorem |
11:15 | |
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Example 1: Evaluate the Algebraic Expression |
11:50 | |
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Example 2: Evaluate the Algebraic Expression |
14:38 | |
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Example 3: Area of a Triangle |
19:11 | |
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Example 4: Fahrenheit to Celsius |
20:41 | |
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Properties of Real Numbers |
20:15 |
| | |
Intro |
0:00 | |
| | |
Real Numbers |
0:07 | |
| | |
| Number Line |
0:15 | |
| | |
| Rational Numbers |
0:46 | |
| | |
| Irrational Numbers |
2:24 | |
| | |
Venn Diagram of Real Numbers |
4:03 | |
| | |
| Irrational Numbers |
5:00 | |
| | |
| Rational Numbers |
5:19 | |
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| Real Number System |
5:27 | |
| | |
| Natural Numbers |
5:32 | |
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| Whole Numbers |
5:53 | |
| | |
| Integers |
6:19 | |
| | |
| Fractions |
6:46 | |
| | |
Properties of Real Numbers |
7:15 | |
| | |
| Commutative Property |
7:34 | |
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| Associative Property |
8:07 | |
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| Identity Property |
9:04 | |
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| Inverse Property |
9:53 | |
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| Distributive Property |
11:03 | |
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Example 1: What Set of Numbers? |
12:21 | |
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Example 2: What Properties Are Used? |
13:56 | |
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Example 3: Multiplicative Inverse |
16:00 | |
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Example 4: Simplify Using Properties |
17:18 | |
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Solving Equations |
19:10 |
| | |
Intro |
0:00 | |
| | |
Translations |
0:06 | |
| | |
| Verbal Expressions and Algebraic Expressions |
0:13 | |
| | |
| Example: Sum of Two Numbers |
0:19 | |
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| Example: Square of a Number |
1:33 | |
| | |
Properties of Equality |
3:20 | |
| | |
| Reflexive Property |
3:30 | |
| | |
| Symmetric Property |
3:42 | |
| | |
| Transitive Property |
4:01 | |
| | |
| Addition Property |
5:01 | |
| | |
| Subtraction Property |
5:37 | |
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| Multiplication Property |
6:02 | |
| | |
| Division Property |
6:30 | |
| | |
Solving Equations |
6:58 | |
| | |
| Example: Using Properties |
7:18 | |
| | |
Solving for a Variable |
8:25 | |
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| Example: Solve for Z |
8:34 | |
| | |
Example 1: Write Algebraic Expression |
10:15 | |
| | |
Example 2: Write Verbal Expression |
11:31 | |
| | |
Example 3: Solve the Equation |
14:05 | |
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Example 4: Simplify Using Properties |
17:26 | |
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Solving Absolute Value Equations |
17:31 |
| | |
Intro |
0:00 | |
| | |
Absolute Value Expressions |
0:09 | |
| | |
| Distance from Zero |
0:18 | |
| | |
| Example: Absolute Value Expression |
0:24 | |
| | |
Absolute Value Equations |
1:50 | |
| | |
| Example: Absolute Value Equation |
2:00 | |
| | |
| Example: Isolate Expression |
3:13 | |
| | |
No Solution |
3:46 | |
| | |
| Empty Set |
3:58 | |
| | |
| Example: No Solution |
4:12 | |
| | |
Number of Solutions |
4:46 | |
| | |
| Check Each Solution |
4:57 | |
| | |
| Example: Two Solutions |
5:05 | |
| | |
| Example: No Solution |
6:18 | |
| | |
| Example: One Solution |
6:28 | |
| | |
Example 1: Evaluate for X |
7:16 | |
| | |
Example 2: Write Verbal Expression |
9:08 | |
| | |
Example 3: Solve the Equation |
12:18 | |
| | |
Example 4: Simplify Using Properties |
13:36 | |
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Solving Inequalities |
17:14 |
| | |
Intro |
0:00 | |
| | |
Properties of Inequalities |
0:08 | |
| | |
| Addition Property |
0:17 | |
| | |
| Example: Using Numbers |
0:30 | |
| | |
| Subtraction Property |
1:03 | |
| | |
| Example: Using Numbers |
1:19 | |
| | |
Multiplication Properties |
1:44 | |
| | |
| C>0 (Positive Number) |
1:50 | |
| | |
| Example: Using Numbers |
2:05 | |
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| C<0 (Negative Number) |
2:40 | |
| | |
| Example: Using Numbers |
3:10 | |
| | |
Division Properties |
4:11 | |
| | |
| C>0 (Positive Number) |
4:15 | |
| | |
| Example: Using Numbers |
4:27 | |
| | |
| C<0 (Negative Number) |
5:21 | |
| | |
| Example: Using Numbers |
5:32 | |
| | |
Describing the Solution Set |
6:10 | |
| | |
| Example: Set Builder Notation |
6:26 | |
| | |
| Example: Graph (Closed Circle) |
7:08 | |
| | |
| Example: Graph (Open Circle) |
7:30 | |
| | |
Example 1: Solve the Inequality |
7:58 | |
| | |
Example 2: Solve the Inequality |
9:06 | |
| | |
Example 3: Solve the Inequality |
10:10 | |
| | |
Example 4: Solve the Inequality |
13:12 | |
| |
Solving Compound and Absolute Value Inequalities |
25:00 |
| | |
Intro |
0:00 | |
| | |
Compound Inequalities |
0:08 | |
| | |
| 'And' and 'Or' |
0:13 | |
| | |
| Example: And |
0:22 | |
| | |
| Example: Or |
1:12 | |
| | |
'And' Inequality |
1:41 | |
| | |
| Intersection |
1:49 | |
| | |
| Example: Numbers |
2:08 | |
| | |
| Example: Inequality |
2:43 | |
| | |
'Or' Inequality |
4:35 | |
| | |
| Example: Union |
4:45 | |
| | |
| Example: Inequality |
5:53 | |
| | |
Absolute Value Inequalities |
7:19 | |
| | |
| Definition of Absolute Value |
7:33 | |
| | |
| Examples: Compound Inequalities |
8:30 | |
| | |
| Example: Complex Inequality |
12:21 | |
| | |
Example 1: Solve the Inequality |
12:54 | |
| | |
Example 2: Solve the Inequality |
17:21 | |
| | |
Example 3: Solve the Inequality |
18:54 | |
| | |
Example 4: Solve the Inequality |
22:15 | |
| II. Linear Relations and Functions |
| |
Relations and Functions |
32:05 |
| | |
Intro |
0:00 | |
| | |
Coordinate Plane |
0:20 | |
| | |
| X-Coordinate and Y-Coordinate |
0:30 | |
| | |
| Example: Coordinate Pairs |
0:37 | |
| | |
| Quadrants |
1:20 | |
| | |
Relations |
2:14 | |
| | |
| Domain and Range |
2:19 | |
| | |
| Set of Ordered Pairs |
2:29 | |
| | |
| As a Table |
2:51 | |
| | |
Functions |
4:21 | |
| | |
| One Element in Range |
4:32 | |
| | |
| Example: Mapping |
4:43 | |
| | |
| Example: Table and Map |
6:26 | |
| | |
One-to-One Functions |
8:01 | |
| | |
| Example: One-to-One |
8:22 | |
| | |
| Example: Not One-to-One |
9:18 | |
| | |
Graphs of Relations |
11:01 | |
| | |
| Discrete and Continuous |
11:12 | |
| | |
| Example: Discrete |
11:22 | |
| | |
| Example: Continuous |
12:30 | |
| | |
Vertical Line Test |
14:09 | |
| | |
| Example: S Curve |
14:29 | |
| | |
| Example: Function |
16:15 | |
| | |
Equations, Relations, and Functions |
17:03 | |
| | |
| Independent Variable and Dependent Variable |
17:16 | |
| | |
Function Notation |
19:11 | |
| | |
| Example: Function Notation |
19:23 | |
| | |
Example 1: Domain and Range |
20:51 | |
| | |
Example 2: Discrete or Continuous |
23:03 | |
| | |
Example 3: Discrete or Continuous |
25:53 | |
| | |
Example 4: Function Notation |
30:05 | |
| |
Linear Equations |
14:46 |
| | |
Intro |
0:00 | |
| | |
Linear Equations and Functions |
0:07 | |
| | |
| Linear Equation |
0:19 | |
| | |
| Example: Linear Equation |
0:29 | |
| | |
| Example: Linear Function |
1:07 | |
| | |
Standard Form |
2:02 | |
| | |
| Integer Constants with No Common Factor |
2:08 | |
| | |
| Example: Standard Form |
2:27 | |
| | |
Graphing with Intercepts |
4:05 | |
| | |
| X-Intercept and Y-Intercept |
4:12 | |
| | |
| Example: Intercepts |
4:26 | |
| | |
| Example: Graphing |
5:14 | |
| | |
Example 1: Linear Function |
7:53 | |
| | |
Example 2: Linear Function |
9:10 | |
| | |
Example 3: Standard Form |
10:04 | |
| | |
Example 4: Graph with Intercepts |
12:25 | |
| |
Slope |
23:07 |
| | |
Intro |
0:00 | |
| | |
Definition of Slope |
0:07 | |
| | |
| Change in Y / Change in X |
0:26 | |
| | |
| Example: Slope of Graph |
0:37 | |
| | |
Interpretation of Slope |
3:07 | |
| | |
| Horizontal Line (0 Slope) |
3:13 | |
| | |
| Vertical Line (Undefined Slope) |
4:52 | |
| | |
| Rises to Right (Positive Slope) |
6:36 | |
| | |
| Falls to Right (Negative Slope) |
6:53 | |
| | |
Parallel Lines |
7:18 | |
| | |
| Example: Not Vertical |
7:30 | |
| | |
| Example: Vertical |
7:58 | |
| | |
Perpendicular Lines |
8:31 | |
| | |
| Example: Perpendicular |
8:42 | |
| | |
Example 1: Slope of Line |
10:32 | |
| | |
Example 2: Graph Line |
11:45 | |
| | |
Example 3: Parallel to Graph |
13:37 | |
| | |
Example 4: Perpendicular to Graph |
17:57 | |
| |
Writing Linear Functions |
23:05 |
| | |
Intro |
0:00 | |
| | |
Slope Intercept Form |
0:11 | |
| | |
| m and b |
0:28 | |
| | |
| Example: Graph Using Slope Intercept |
0:43 | |
| | |
Point Slope Form |
2:41 | |
| | |
| Relation to Slope Formula |
3:03 | |
| | |
| Example: Point Slope Form |
4:36 | |
| | |
Parallel and Perpendicular Lines |
6:28 | |
| | |
| Review of Parallel and Perpendicular Lines |
6:31 | |
| | |
| Example: Parallel |
7:50 | |
| | |
| Example: Perpendicular |
9:58 | |
| | |
Example 1: Slope Intercept Form |
11:07 | |
| | |
Example 2: Slope Intercept Form |
13:07 | |
| | |
Example 3: Parallel |
15:49 | |
| | |
Example 4: Perpendicular |
18:42 | |
| |
Special Functions |
31:05 |
| | |
Intro |
0:00 | |
| | |
Step Functions |
0:07 | |
| | |
| Example: Apple Prices |
0:30 | |
| | |
Absolute Value Function |
4:55 | |
| | |
| Example: Absolute Value |
5:05 | |
| | |
Piecewise Functions |
9:08 | |
| | |
| Example: Piecewise |
9:27 | |
| | |
Example 1: Absolute Value Function |
14:00 | |
| | |
Example 2: Absolute Value Function |
20:39 | |
| | |
Example 3: Piecewise Function |
22:26 | |
| | |
Example 4: Step Function |
25:25 | |
| |
Graphing Inequalities |
21:42 |
| | |
Intro |
0:00 | |
| | |
Graphing Linear Inequalities |
0:07 | |
| | |
| Shaded Region |
0:19 | |
| | |
| Using Test Points |
0:32 | |
| | |
| Graph Corresponding Linear Function |
0:46 | |
| | |
| Dashed or Solid Lines |
0:59 | |
| | |
| Use Test Point |
1:21 | |
| | |
| Example: Linear Inequality |
1:58 | |
| | |
Graphing Absolute Value Inequalities |
4:50 | |
| | |
| Graph Corresponding Equations |
4:59 | |
| | |
| Use Test Point |
5:20 | |
| | |
| Example: Absolute Value Inequality |
5:38 | |
| | |
Example 1: Linear Inequality |
9:17 | |
| | |
Example 2: Linear Inequality |
11:56 | |
| | |
Example 3: Linear Inequality |
14:29 | |
| | |
Example 4: Absolute Value Inequality |
17:06 | |
| III. Systems of Equations and Inequalities |
| |
Solving Systems of Equations by Graphing |
17:13 |
| | |
Intro |
0:00 | |
| | |
Systems of Equations |
0:09 | |
| | |
| Example: Two Equations |
0:24 | |
| | |
Solving by Graphing |
0:53 | |
| | |
| Point of Intersection |
1:09 | |
| | |
Types of Systems |
2:29 | |
| | |
| Independent (Single Solution) |
2:34 | |
| | |
| Dependent (Infinite Solutions) |
3:05 | |
| | |
| Inconsistent (No Solution) |
4:23 | |
| | |
Example 1: Solve by Graphing |
5:20 | |
| | |
Example 2: Solve by Graphing |
9:10 | |
| | |
Example 3: Solve by Graphing |
12:27 | |
| | |
Example 4: Solve by Graphing |
14:54 | |
| |
Solving Systems of Equations Algebraically |
23:53 |
| | |
Intro |
0:00 | |
| | |
Solving by Substitution |
0:08 | |
| | |
| Example: System of Equations |
0:36 | |
| | |
Solving by Multiplication |
7:22 | |
| | |
| Extra Step of Multiplying |
7:38 | |
| | |
| Example: System of Equations |
8:00 | |
| | |
Inconsistent and Dependent Systems |
11:14 | |
| | |
| Variables Drop Out |
11:48 | |
| | |
| Inconsistent System (Never True) |
12:01 | |
| | |
| Constant Equals Constant |
12:53 | |
| | |
| Dependent System (Always True) |
13:11 | |
| | |
Example 1: Solve Algebraically |
13:58 | |
| | |
Example 2: Solve Algebraically |
15:52 | |
| | |
Example 3: Solve Algebraically |
17:54 | |
| | |
Example 4: Solve Algebraically |
21:40 | |
| |
Solving Systems of Inequalities By Graphing |
27:12 |
| | |
Intro |
0:00 | |
| | |
Solving by Graphing |
0:08 | |
| | |
| Graph Each Inequality |
0:25 | |
| | |
| Overlap |
0:35 | |
| | |
| Corresponding Linear Equations |
1:03 | |
| | |
| Test Point |
1:23 | |
| | |
| Example: System of Inequalities |
1:51 | |
| | |
No Solution |
7:06 | |
| | |
| Empty Set |
7:26 | |
| | |
| Example: No Solution |
7:34 | |
| | |
Example 1: Solve by Graphing |
10:27 | |
| | |
Example 2: Solve by Graphing |
13:30 | |
| | |
Example 3: Solve by Graphing |
17:19 | |
| | |
Example 4: Solve by Graphing |
23:23 | |
| |
Solving Systems of Equations in Three Variables |
28:53 |
| | |
Intro |
0:00 | |
| | |
Solving Systems in Three Variables |
0:17 | |
| | |
| Triple of Values |
0:31 | |
| | |
| Example: Three Variables |
0:56 | |
| | |
Number of Solutions |
5:55 | |
| | |
| One Solution |
6:08 | |
| | |
| No Solution |
6:24 | |
| | |
| Infinite Solutions |
7:06 | |
| | |
Example 1: Solve 3 Variables |
7:59 | |
| | |
Example 2: Solve 3 Variables |
13:50 | |
| | |
Example 3: Solve 3 Variables |
19:54 | |
| | |
Example 4: Solve 3 Variables |
25:50 | |
| IV. Matrices |
| |
Basic Matrix Concepts |
11:34 |
| | |
Intro |
0:00 | |
| | |
What is a Matrix |
0:26 | |
| | |
| Brackets |
0:46 | |
| | |
| Designation |
1:21 | |
| | |
| Element |
1:47 | |
| | |
| Matrix Equations |
1:59 | |
| | |
Dimensions |
2:27 | |
| | |
| Rows (m) and Columns (n) |
2:37 | |
| | |
| Examples: Dimensions |
2:43 | |
| | |
Special Matrices |
4:22 | |
| | |
| Row Matrix |
4:32 | |
| | |
| Column Matrix |
5:00 | |
| | |
| Zero Matrix |
6:00 | |
| | |
Equal Matrices |
6:30 | |
| | |
| Example: Corresponding Elements |
6:36 | |
| | |
Example 1: Matrix Dimension |
8:12 | |
| | |
Example 2: Matrix Dimension |
9:03 | |
| | |
Example 3: Zero Matrix |
9:38 | |
| | |
Example 4: Row and Column Matrix |
10:26 | |
| |
Matrix Operations |
21:36 |
| | |
Intro |
0:00 | |
| | |
Matrix Addition |
0:18 | |
| | |
| Same Dimensions |
0:25 | |
| | |
| Example: Adding Matrices |
1:04 | |
| | |
Matrix Subtraction |
3:42 | |
| | |
| Same Dimensions |
3:48 | |
| | |
| Example: Subtracting Matrices |
4:04 | |
| | |
Scalar Multiplication |
6:08 | |
| | |
| Scalar Constant |
6:24 | |
| | |
| Example: Multiplying Matrices |
6:32 | |
| | |
Properties of Matrix Operations |
8:23 | |
| | |
| Commutative Property |
8:41 | |
| | |
| Associative Property |
9:08 | |
| | |
| Distributive Property |
9:44 | |
| | |
Example 1: Matrix Addition |
10:24 | |
| | |
Example 2: Matrix Subtraction |
11:58 | |
| | |
Example 3: Scalar Multiplication |
14:23 | |
| | |
Example 4: Matrix Properties |
16:09 | |
| |
Matrix Multiplication |
29:36 |
| | |
Intro |
0:00 | |
| | |
Dimension Requirement |
0:17 | |
| | |
| n = p |
0:24 | |
| | |
| Resulting Product Matrix (m x q) |
1:21 | |
| | |
| Example: Multiplication |
1:54 | |
| | |
Matrix Multiplication |
3:38 | |
| | |
| Example: Matrix Multiplication |
4:07 | |
| | |
Properties of Matrix Multiplication |
10:46 | |
| | |
| Associative Property |
11:00 | |
| | |
| Associative Property (Scalar) |
11:28 | |
| | |
| Distributive Property |
12:06 | |
| | |
| Distributive Property (Scalar) |
12:30 | |
| | |
Example 1: Possible Matrices |
13:31 | |
| | |
Example 2: Multiplying Matrices |
17:08 | |
| | |
Example 3: Multiplying Matrices |
20:41 | |
| | |
Example 4: Matrix Properties |
24:41 | |
| |
Determinants |
33:13 |
| | |
Intro |
0:00 | |
| | |
What is a Determinant |
0:13 | |
| | |
| Square Matrices |
0:23 | |
| | |
| Vertical Bars |
0:41 | |
| | |
Determinant of a 2x2 Matrix |
1:21 | |
| | |
| Second Order Determinant |
1:37 | |
| | |
| Formula |
1:45 | |
| | |
| Example: 2x2 Determinant |
1:58 | |
| | |
Determinant of a 3x3 Matrix |
2:50 | |
| | |
| Expansion by Minors |
3:08 | |
| | |
| Third Order Determinant |
3:19 | |
| | |
| Expanding Row One |
4:06 | |
| | |
| Example: 3x3 Determinant |
6:40 | |
| | |
Diagonal Method for 3x3 Matrices |
13:24 | |
| | |
| Example: Diagonal Method |
13:36 | |
| | |
Example 1: Determinant of 2x2 |
18:59 | |
| | |
Example 2: Determinant of 3x3 |
20:03 | |
| | |
Example 3: Determinant of 3x3 |
25:35 | |
| | |
Example 4: Determinant of 3x3 |
29:22 | |
| |
Cramer's Rule |
28:25 |
| | |
Intro |
0:00 | |
| | |
System of Two Equations in Two Variables |
0:16 | |
| | |
| One Variable |
0:50 | |
| | |
| Determinant of Denominator |
1:14 | |
| | |
| Determinants of Numerators |
2:23 | |
| | |
| Example: System of Equations |
3:34 | |
| | |
System of Three Equations in Three Variables |
7:06 | |
| | |
| Determinant of Denominator |
7:17 | |
| | |
| Determinants of Numerators |
7:52 | |
| | |
Example 1: Two Equations |
8:57 | |
| | |
Example 2: Two Equations |
13:21 | |
| | |
Example 3: Three Equations |
17:11 | |
| | |
Example 4: Three Equations |
23:43 | |
| |
Identity and Inverse Matrices |
22:25 |
| | |
Intro |
0:00 | |
| | |
Identity Matrix |
0:13 | |
| | |
| Example: 2x2 Identity Matrix |
0:30 | |
| | |
| Example: 4x4 Identity Matrix |
0:50 | |
| | |
| Properties of Identity Matrices |
1:24 | |
| | |
| Example: Multiplying Identity Matrix |
2:52 | |
| | |
Matrix Inverses |
5:30 | |
| | |
| Writing Matrix Inverse |
6:07 | |
| | |
Inverse of a 2x2 Matrix |
6:39 | |
| | |
| Example: 2x2 Matrix |
7:31 | |
| | |
Example 1: Inverse Matrix |
10:18 | |
| | |
Example 2: Find the Inverse Matrix |
13:04 | |
| | |
Example 3: Find the Inverse Matrix |
17:53 | |
| | |
Example 4: Find the Inverse Matrix |
20:44 | |
| |
Solving Systems of Equations Using Matrices |
22:32 |
| | |
Intro |
0:00 | |
| | |
Matrix Equations |
0:11 | |
| | |
| Example: System of Equations |
0:21 | |
| | |
Solving Systems of Equations |
4:01 | |
| | |
| Isolate x |
4:16 | |
| | |
| Example: Using Numbers |
5:10 | |
| | |
| Multiplicative Inverse |
5:54 | |
| | |
Example 1: Write as Matrix Equation |
7:18 | |
| | |
Example 2: Use Matrix Equations |
9:12 | |
| | |
Example 3: Use Matrix Equations |
15:06 | |
| | |
Example 4: Use Matrix Equations |
19:35 | |
| V. Quadratic Functions and Inequalities |
| |
Graphing Quadratic Functions |
31:48 |
| | |
Intro |
0:00 | |
| | |
Quadratic Functions |
0:12 | |
| | |
| A is Zero |
0:27 | |
| | |
| Example: Parabola |
0:45 | |
| | |
Properties of Parabolas |
2:08 | |
| | |
| Axis of Symmetry |
2:11 | |
| | |
| Vertex |
2:32 | |
| | |
| Example: Parabola |
2:48 | |
| | |
Minimum and Maximum Values |
9:02 | |
| | |
| Positive or Negative |
9:28 | |
| | |
| Upward or Downward |
9:58 | |
| | |
| Example: Minimum |
10:31 | |
| | |
| Example: Maximum |
11:16 | |
| | |
Example 1: Axis of Symmetry, Vertex, Graph |
12:41 | |
| | |
Example 2: Axis of Symmetry, Vertex, Graph |
17:25 | |
| | |
Example 3: Minimum or Maximum |
21:47 | |
| | |
Example 4: Minimum or Maximum |
27:09 | |
| |
Solving Quadratic Equations by Graphing |
27:03 |
| | |
Intro |
0:00 | |
| | |
Quadratic Equations |
0:16 | |
| | |
| Standard Form |
0:18 | |
| | |
| Example: Quadratic Equation |
0:47 | |
| | |
Solving by Graphing |
1:41 | |
| | |
| Roots (x-Intercepts) |
1:48 | |
| | |
| Example: Number of Solutions |
2:12 | |
| | |
Estimating Solutions |
9:23 | |
| | |
| Example: Integer Solutions |
9:30 | |
| | |
| Example: Estimating |
9:53 | |
| | |
Example 1: Solve by Graphing |
10:52 | |
| | |
Example 2: Solve by Graphing |
15:10 | |
| | |
Example 1: Solve by Graphing |
17:50 | |
| | |
Example 1: Solve by Graphing |
20:54 | |
| |
Solving Quadratic Equations by Factoring |
19:53 |
| | |
Intro |
0:00 | |
| | |
Factoring Techniques |
0:15 | |
| | |
| Greatest Common Factor (GCF) |
0:37 | |
| | |
| Difference of Two Squares |
1:48 | |
| | |
| Perfect Square Trinomials |
2:30 | |
| | |
| General Trinomials |
3:09 | |
| | |
Zero Product Rule |
5:22 | |
| | |
| Example: Zero Product |
5:53 | |
| | |
Example 1: Solve by Factoring |
7:46 | |
| | |
Example 1: Solve by Factoring |
9:48 | |
| | |
Example 1: Solve by Factoring |
12:34 | |
| | |
Example 1: Solve by Factoring |
15:28 | |
| |
Imaginary and Complex Numbers |
35:45 |
| | |
Intro |
0:00 | |
| | |
Properties of Square Roots |
0:10 | |
| | |
| Product Property |
0:26 | |
| | |
| Example: Product Property |
0:56 | |
| | |
| Quotient Property |
2:17 | |
| | |
| Example: Quotient Property |
2:35 | |
| | |
Imaginary Numbers |
3:12 | |
| | |
| Imaginary 'i' |
3:51 | |
| | |
| Examples: Imaginary Number |
4:22 | |
| | |
Complex Numbers |
7:23 | |
| | |
| Real Part and Imaginary Part |
7:33 | |
| | |
| Examples: Complex Numbers |
7:57 | |
| | |
Equality |
9:37 | |
| | |
| Example: Equal Complex Numbers |
9:52 | |
| | |
Addition and Subtraction |
10:12 | |
| | |
| Examples: Adding Complex Numbers |
10:25 | |
| | |
Complex Plane |
13:32 | |
| | |
| Horizontal Axis (Real) |
13:49 | |
| | |
| Vertical Axis (Imaginary) |
13:59 | |
| | |
| Example: Labeling |
14:11 | |
| | |
Multiplication |
15:57 | |
| | |
| Example: FOIL Method |
16:03 | |
| | |
Division |
18:37 | |
| | |
| Complex Conjugates |
18:45 | |
| | |
| Conjugate Pairs |
19:10 | |
| | |
| Example: Dividing Complex Numbers |
20:00 | |
| | |
Example 1: Simplify Complex Number |
24:50 | |
| | |
Example 2: Simplify Complex Number |
27:56 | |
| | |
Example 3: Multiply Complex Numbers |
29:27 | |
| | |
Example 3: Dividing Complex Numbers |
31:48 | |
| |
Completing the Square |
27:11 |
| | |
Intro |
0:00 | |
| | |
Square Root Property |
0:12 | |
| | |
| Example: Perfect Square |
0:38 | |
| | |
| Example: Perfect Square Trinomial |
3:00 | |
| | |
Completing the Square |
4:39 | |
| | |
| Constant Term |
4:50 | |
| | |
| Example: Complete the Square |
5:04 | |
| | |
Solve Equations |
6:42 | |
| | |
| Add to Both Sides |
6:59 | |
| | |
| Example: Complete the Square |
7:07 | |
| | |
Equations Where 'a' Not Equal to 1 |
10:58 | |
| | |
| Divide by Coefficient |
11:08 | |
| | |
| Example: Complete the Square |
11:24 | |
| | |
Complex Solutions |
14:05 | |
| | |
| Real and Imaginary |
14:14 | |
| | |
| Example: Complex Solution |
14:35 | |
| | |
Example 1: Square Root Property |
18:31 | |
| | |
Example 2: Complete the Square |
19:15 | |
| | |
Example 3: Complete the Square |
20:40 | |
| | |
Example 4: Complete the Square |
23:56 | |
| |
Quadratic Formula and the Discriminant |
22:48 |
| | |
Intro |
0:00 | |
| | |
Quadratic Formula |
0:21 | |
| | |
| Standard Form |
0:29 | |
| | |
| Example: Quadratic Formula |
0:57 | |
| | |
One Rational Root |
3:00 | |
| | |
| Example: One Root |
3:31 | |
| | |
Complex Solutions |
6:16 | |
| | |
| Complex Conjugate |
6:28 | |
| | |
| Example: Complex Solution |
7:15 | |
| | |
Discriminant |
9:42 | |
| | |
| Positive Discriminant |
10:03 | |
| | |
| Perfect Square (Rational) |
10:51 | |
| | |
| Not Perfect Square (2 Irrational) |
11:27 | |
| | |
| Negative Discriminant |
12:28 | |
| | |
| Zero Discriminant |
12:57 | |
| | |
Example 1: Quadratic Formula |
13:50 | |
| | |
Example 2: Quadratic Formula |
16:03 | |
| | |
Example 3: Quadratic Formula |
19:00 | |
| | |
Example 4: Discriminant |
21:33 | |
| |
Analyzing the Graphs of Quadratic Functions |
30:07 |
| | |
Intro |
0:00 | |
| | |
Vertex Form |
0:12 | |
| | |
| H and K |
0:32 | |
| | |
| Axis of Symmetry |
0:36 | |
| | |
| Vertex |
0:42 | |
| | |
| Example: Origin |
1:00 | |
| | |
| Example: k = 2 |
2:12 | |
| | |
| Example: h = 1 |
4:27 | |
| | |
Significance of Coefficient 'a' |
7:13 | |
| | |
| Example: |a| > 1 |
7:25 | |
| | |
| Example: |a| < 1 |
8:18 | |
| | |
| Example: |a| > 0 |
8:51 | |
| | |
| Example: |a| < 0 |
9:05 | |
| | |
Writing Quadratic Equations in Vertex Form |
10:22 | |
| | |
| Standard Form to Vertex Form |
10:35 | |
| | |
| Example: Standard Form |
11:02 | |
| | |
| Example: 'a' Term Not 1 |
14:42 | |
| | |
Example 1: Vertex Form |
19:47 | |
| | |
Example 2: Vertex Form |
22:09 | |
| | |
Example 3: Vertex Form |
24:32 | |
| | |
Example 4: Vertex Form |
28:23 | |
| |
Graphing and Solving Quadratic Inequalities |
27:05 |
| | |
Intro |
0:00 | |
| | |
Graphing Quadratic Inequalities |
0:11 | |
| | |
| Test Point |
0:18 | |
| | |
| Example: Quadratic Inequality |
0:29 | |
| | |
Solving Quadratic Inequalities |
3:57 | |
| | |
| Example: Parameter |
4:24 | |
| | |
Example 1: Graph Inequality |
11:16 | |
| | |
Example 2: Solve Inequality |
14:27 | |
| | |
Example 3: Graph Inequality |
19:14 | |
| | |
Example 4: Solve Inequality |
23:48 | |
| VI. Polynomial Functions |
| |
Properties of Exponents |
19:29 |
| | |
Intro |
0:00 | |
| | |
Simplifying Exponential Expressions |
0:09 | |
| | |
| Monomial Simplest Form |
0:19 | |
| | |
Negative Exponents |
1:07 | |
| | |
| Examples: Simple |
1:34 | |
| | |
Properties of Exponents |
3:06 | |
| | |
| Negative Exponents |
3:13 | |
| | |
| Multiplying Same Base |
3:24 | |
| | |
| Dividing Same Base |
3:45 | |
| | |
| Raising Power to a Power |
4:33 | |
| | |
| Parentheses (Multiplying) |
5:11 | |
| | |
| Parentheses (Dividing) |
5:47 | |
| | |
| Raising to 0th Power |
6:15 | |
| | |
Example 1: Simplify Exponents |
7:59 | |
| | |
Example 2: Simplify Exponents |
10:41 | |
| | |
Example 3: Simplify Exponents |
14:11 | |
| | |
Example 4: Simplify Exponents |
18:04 | |
| |
Operations on Polynomials |
13:27 |
| | |
Intro |
0:00 | |
| | |
Adding and Subtracting Polynomials |
0:13 | |
| | |
| Like Terms and Like Monomials |
0:23 | |
| | |
| Examples: Adding Monomials |
1:14 | |
| | |
Multiplying Polynomials |
3:40 | |
| | |
| Distributive Property |
3:44 | |
| | |
| Example: Monomial by Polynomial |
4:06 | |
| | |
Example 1: Simplify Polynomials |
5:47 | |
| | |
Example 2: Simplify Polynomials |
6:28 | |
| | |
Example 3: Simplify Polynomials |
8:38 | |
| | |
Example 4: Simplify Polynomials |
10:47 | |
| |
Dividing Polynomials |
31:11 |
| | |
Intro |
0:00 | |
| | |
Dividing by a Monomial |
0:13 | |
| | |
| Example: Numbers |
0:26 | |
| | |
| Example: Polynomial by a Monomial |
1:18 | |
| | |
Long Division |
2:28 | |
| | |
| Remainder Term |
2:41 | |
| | |
| Example: Dividing with Numbers |
3:04 | |
| | |
| Example: With Polynomials |
5:01 | |
| | |
| Example: Missing Terms |
7:58 | |
| | |
Synthetic Division |
11:44 | |
| | |
| Restriction |
12:04 | |
| | |
| Example: Divisor in Form |
12:20 | |
| | |
Divisor in Synthetic Division |
15:54 | |
| | |
| Example: Coefficient to 1 |
16:07 | |
| | |
Example 1: Divide Polynomials |
17:10 | |
| | |
Example 2: Divide Polynomials |
19:08 | |
| | |
Example 3: Synthetic Division |
21:42 | |
| | |
Example 4: Synthetic Division |
25:09 | |
| |
Polynomial Functions |
22:30 |
| | |
Intro |
0:00 | |
| | |
Polynomial in One Variable |
0:13 | |
| | |
| Leading Coefficient |
0:27 | |
| | |
| Example: Polynomial |
1:18 | |
| | |
| Degree |
1:31 | |
| | |
Polynomial Functions |
2:57 | |
| | |
| Example: Function |
3:13 | |
| | |
Function Values |
3:33 | |
| | |
| Example: Numerical Values |
3:53 | |
| | |
| Example: Algebraic Expressions |
5:11 | |
| | |
Zeros of Polynomial Functions |
5:50 | |
| | |
| Odd Degree |
6:04 | |
| | |
| Even Degree |
7:29 | |
| | |
End Behavior |
8:28 | |
| | |
| Even Degrees |
9:09 | |
| | |
| Example: Leading Coefficient +/- |
9:23 | |
| | |
| Odd Degrees |
12:51 | |
| | |
| Example: Leading Coefficient +/- |
13:00 | |
| | |
Example 1: Degree and Leading Coefficient |
15:03 | |
| | |
Example 2: Polynomial Function |
15:56 | |
| | |
Example 3: Polynomial Function |
17:34 | |
| | |
Example 4: End Behavior |
19:53 | |
| |
Analyzing Graphs of Polynomial Functions |
33:29 |
| | |
Intro |
0:00 | |
| | |
Graphing Polynomial Functions |
0:11 | |
| | |
| Example: Table and End Behavior |
0:39 | |
| | |
Location Principle |
4:43 | |
| | |
| Zero Between Two Points |
5:03 | |
| | |
| Example: Location Principle |
5:21 | |
| | |
Maximum and Minimum Points |
8:40 | |
| | |
| Relative Maximum and Relative Minimum |
9:16 | |
| | |
| Example: Number of Relative Max/Min |
11:11 | |
| | |
Example 1: Graph Polynomial Function |
11:57 | |
| | |
Example 2: Graph Polynomial Function |
16:19 | |
| | |
Example 3: Graph Polynomial Function |
23:27 | |
| | |
Example 4: Graph Polynomial Function |
28:35 | |
| |
Solving Polynomial Functions |
21:10 |
| | |
Intro |
0:00 | |
| | |
Factoring Polynomials |
0:06 | |
| | |
| Greatest Common Factor (GCF) |
0:25 | |
| | |
| Difference of Two Squares |
1:14 | |
| | |
| Perfect Square Trinomials |
2:07 | |
| | |
| General Trinomials |
2:57 | |
| | |
| Grouping |
4:32 | |
| | |
Sum and Difference of Two Cubes |
6:03 | |
| | |
| Examples: Two Cubes |
6:14 | |
| | |
Quadratic Form |
8:22 | |
| | |
| Example: Quadratic Form |
8:44 | |
| | |
Example 1: Factor Polynomial |
12:03 | |
| | |
Example 2: Factor Polynomial |
13:54 | |
| | |
Example 3: Quadratic Form |
15:33 | |
| | |
Example 4: Solve Polynomial Function |
17:24 | |
| |
Remainder and Factor Theorems |
31:21 |
| | |
Intro |
0:00 | |
| | |
Remainder Theorem |
0:07 | |
| | |
| Checking Work |
0:22 | |
| | |
| Dividend and Divisor in Theorem |
1:12 | |
| | |
| Example: f(a) |
2:05 | |
| | |
Synthetic Substitution |
5:43 | |
| | |
| Example: Polynomial Function |
6:15 | |
| | |
Factor Theorem |
9:54 | |
| | |
| Example: Numbers |
10:16 | |
| | |
| Example: Confirm Factor |
11:27 | |
| | |
Factoring Polynomials |
14:48 | |
| | |
| Example: 3rd Degree Polynomial |
15:07 | |
| | |
Example 1: Remainder Theorem |
19:17 | |
| | |
Example 2: Other Factors |
21:57 | |
| | |
Example 3: Remainder Theorem |
25:52 | |
| | |
Example 4: Other Factors |
28:21 | |
| |
Roots and Zeros |
31:27 |
| | |
Intro |
0:00 | |
| | |
Number of Roots |
0:08 | |
| | |
| Not Nature of Roots |
0:18 | |
| | |
| Example: Real and Complex Roots |
0:25 | |
| | |
Descartes' Rule of Signs |
2:05 | |
| | |
| Positive Real Roots |
2:21 | |
| | |
| Example: Positive |
2:39 | |
| | |
| Negative Real Roots |
5:44 | |
| | |
| Example: Negative |
6:06 | |
| | |
Finding the Roots |
9:59 | |
| | |
| Example: Combination of Real and Complex |
10:07 | |
| | |
Conjugate Roots |
13:18 | |
| | |
| Example: Conjugate Roots |
13:50 | |
| | |
Example 1: Solve Polynomial |
16:03 | |
| | |
Example 2: Solve Polynomial |
18:36 | |
| | |
Example 3: Possible Combinations |
23:13 | |
| | |
Example 4: Possible Combinations |
27:11 | |
| |
Rational Zero Theorem |
31:16 |
| | |
Intro |
0:00 | |
| | |
Equation |
0:08 | |
| | |
| List of Possibilities |
0:16 | |
| | |
| Equation with Constant and Leading Coefficient |
1:04 | |
| | |
| Example: Rational Zero |
2:46 | |
| | |
Leading Coefficient Equal to One |
7:19 | |
| | |
| Equation with Leading Coefficient of One |
7:34 | |
| | |
| Example: Coefficient Equal to 1 |
8:45 | |
| | |
Finding Rational Zeros |
12:58 | |
| | |
| Division with Remainder Zero |
13:32 | |
| | |
Example 1: Possible Rational Zeros |
14:20 | |
| | |
Example 2: Possible Rational Zeros |
16:02 | |
| | |
Example 3: Possible Rational Zeros |
19:58 | |
| | |
Example 4: Find All Zeros |
22:06 | |
| VII. Radical Expressions and Inequalities |
| |
Operations on Functions |
34:30 |
| | |
Intro |
0:00 | |
| | |
Arithmetic Operations |
0:07 | |
| | |
| Domain |
0:16 | |
| | |
| Intersection |
0:24 | |
| | |
| Denominator is Zero |
0:49 | |
| | |
| Example: Operations |
1:02 | |
| | |
Composition of Functions |
7:18 | |
| | |
| Notation |
7:48 | |
| | |
| Right to Left |
8:18 | |
| | |
| Example: Composition |
8:48 | |
| | |
Composition is Not Commutative |
17:23 | |
| | |
| Example: Not Commutative |
17:51 | |
| | |
Example 1: Function Operations |
20:55 | |
| | |
Example 2: Function Operations |
24:34 | |
| | |
Example 3: Compositions |
27:51 | |
| | |
Example 4: Function Operations |
31:09 | |
| |
Inverse Functions and Relations |
22:42 |
| | |
Intro |
0:00 | |
| | |
Inverse of a Relation |
0:14 | |
| | |
| Example: Ordered Pairs |
0:56 | |
| | |
Inverse of a Function |
3:24 | |
| | |
| Domain and Range Switched |
3:52 | |
| | |
| Example: Inverse |
4:28 | |
| | |
Procedure to Construct an Inverse Function |
6:42 | |
| | |
| f(x) to y |
6:42 | |
| | |
| Interchange x and y |
6:59 | |
| | |
| Solve for y |
7:06 | |
| | |
| Write Inverse f(x) for y |
7:14 | |
| | |
| Example: Inverse Function |
7:25 | |
| | |
| Example: Inverse Function 2 |
8:48 | |
| | |
Inverses and Compositions |
10:44 | |
| | |
| Example: Inverse Composition |
11:46 | |
| | |
Example 1: Inverse Relation |
14:49 | |
| | |
Example 2: Inverse of Function |
15:40 | |
| | |
Example 3: Inverse of Function |
17:06 | |
| | |
Example 4: Inverse Functions |
18:55 | |
| |
Square Root Functions and Inequalities |
30:04 |
| | |
Intro |
0:00 | |
| | |
Square Root Functions |
0:07 | |
| | |
| Examples: Square Root Function |
0:16 | |
| | |
| Example: Not Square Root Function |
0:46 | |
| | |
| Radicand |
1:12 | |
| | |
| Example: Restriction |
1:31 | |
| | |
Graphing Square Root Functions |
3:42 | |
| | |
| Example: Graphing |
3:49 | |
| | |
Square Root Inequalities |
8:47 | |
| | |
| Same Technique |
9:00 | |
| | |
| Example: Square Root Inequality |
9:20 | |
| | |
Example 1: Graph Square Root Function |
15:19 | |
| | |
Example 2: Graph Square Root Function |
18:03 | |
| | |
Example 3: Graph Square Root Function |
22:41 | |
| | |
Example 4: Square Root Inequalities |
25:37 | |
| |
nth Roots |
20:46 |
| | |
Intro |
0:00 | |
| | |
Definition of the nth Root |
0:07 | |
| | |
| Example: 5th Root |
0:20 | |
| | |
| Example: 6th Root |
0:51 | |
| | |
Principal nth Root |
1:39 | |
| | |
| Example: Principal Roots |
2:06 | |
| | |
Using Absolute Values |
5:58 | |
| | |
| Example: Square Root |
6:18 | |
| | |
| Example: 6th Root |
8:40 | |
| | |
| Example: Negative |
10:15 | |
| | |
Example 1: Simplify Radicals |
12:23 | |
| | |
Example 2: Simplify Radicals |
13:29 | |
| | |
Example 3: Simplify Radicals |
16:07 | |
| | |
Example 4: Simplify Radicals |
18:18 | |
| |
Operations with Radical Expressions |
41:11 |
| | |
Intro |
0:00 | |
| | |
Properties of Radicals |
0:16 | |
| | |
| Quotient Property |
0:29 | |
| | |
| Example: Quotient |
1:00 | |
| | |
| Example: Product Property |
1:47 | |
| | |
Simplifying Radical Expressions |
3:24 | |
| | |
| Radicand No nth Powers |
3:47 | |
| | |
| Radicand No Fractions |
6:33 | |
| | |
| No Radicals in Denominator |
7:16 | |
| | |
Rationalizing Denominators |
8:27 | |
| | |
| Example: Radicand nth Power |
9:05 | |
| | |
Conjugate Radical Expressions |
11:47 | |
| | |
| Conjugates |
12:07 | |
| | |
| Example: Conjugate Radical Expression |
13:11 | |
| | |
Adding and Subtracting Radicals |
16:12 | |
| | |
| Same Index, Same Radicand |
16:20 | |
| | |
| Example: Like Radicals |
16:28 | |
| | |
Multiplying Radicals |
19:04 | |
| | |
| Distributive Property |
19:10 | |
| | |
| Example: Multiplying Radicals |
19:20 | |
| | |
Example 1: Simplify Radical |
24:11 | |
| | |
Example 2: Simplify Radicals |
28:43 | |
| | |
Example 3: Simplify Radicals |
32:00 | |
| | |
Example 4: Simplify Radical |
36:34 | |
| |
Rational Exponents |
30:45 |
| | |
Intro |
0:00 | |
| | |
Definition 1 |
0:20 | |
| | |
| Example: Using Numbers |
0:39 | |
| | |
| Example: Non-Negative |
2:46 | |
| | |
| Example: Odd |
3:34 | |
| | |
Definition 2 |
4:32 | |
| | |
| Restriction |
4:52 | |
| | |
| Example: Relate to Definition 1 |
5:04 | |
| | |
| Example: m Not 1 |
5:31 | |
| | |
Simplifying Expressions |
7:53 | |
| | |
| Multiplication |
8:31 | |
| | |
| Division |
9:29 | |
| | |
| Multiply Exponents |
10:08 | |
| | |
| Raised Power |
11:05 | |
| | |
| Zero Power |
11:29 | |
| | |
| Negative Power |
11:49 | |
| | |
Simplified Form |
13:52 | |
| | |
| Complex Fraction |
14:16 | |
| | |
| Negative Exponents |
14:40 | |
| | |
| Example: More Complicated |
15:14 | |
| | |
Example 1: Write as Radical |
19:03 | |
| | |
Example 2: Write with Rational Exponents |
20:40 | |
| | |
Example 3: Complex Fraction |
22:09 | |
| | |
Example 4: Complex Fraction |
26:22 | |
| |
Solving Radical Equations and Inequalities |
31:27 |
| | |
Intro |
0:00 | |
| | |
Radical Equations |
0:11 | |
| | |
| Variables in Radicands |
0:22 | |
| | |
| Example: Radical Equation |
1:06 | |
| | |
| Example: Complex Equation |
2:42 | |
| | |
Extraneous Roots |
7:21 | |
| | |
| Squaring Technique |
7:35 | |
| | |
| Double Check |
7:44 | |
| | |
| Example: Extraneous |
8:21 | |
| | |
Eliminating nth Roots |
10:04 | |
| | |
| Isolate and Raise Power |
10:14 | |
| | |
| Example: nth Root |
10:27 | |
| | |
Radical Inequalities |
11:27 | |
| | |
| Restriction: Index is Even |
11:53 | |
| | |
| Example: Radical Inequality |
12:29 | |
| | |
Example 1: Solve Radical Equation |
15:41 | |
| | |
Example 2: Solve Radical Equation |
17:44 | |
| | |
Example 3: Solve Radical Inequality |
20:24 | |
| | |
Example 4: Solve Radical Equation |
24:34 | |
| VIII. Rational Equations and Inequalities |
| |
Multiplying and Dividing Rational Expressions |
40:54 |
| | |
Intro |
0:00 | |
| | |
Simplifying Rational Expressions |
0:22 | |
| | |
| Algebraic Fraction |
0:29 | |
| | |
| Examples: Rational Expressions |
0:49 | |
| | |
| Example: GCF |
1:33 | |
| | |
| Example: Simplify Rational Expression |
2:26 | |
| | |
Factoring -1 |
4:04 | |
| | |
| Example: Simplify with -1 |
4:19 | |
| | |
Multiplying and Dividing Rational Expressions |
6:59 | |
| | |
| Multiplying and Dividing |
7:28 | |
| | |
| Example: Multiplying Rational Expressions |
8:36 | |
| | |
| Example: Dividing Rational Expressions |
11:20 | |
| | |
Factoring |
14:01 | |
| | |
| Factoring Polynomials |
14:19 | |
| | |
| Example: Factoring |
14:35 | |
| | |
Complex Fractions |
18:22 | |
| | |
| Example: Numbers |
18:37 | |
| | |
| Example: Algebraic Complex Fractions |
19:25 | |
| | |
Example 1: Simplify Rational Expression |
25:56 | |
| | |
Example 2: Simplify Rational Expression |
29:34 | |
| | |
Example 3: Simplify Rational Expression |
31:39 | |
| | |
Example 4: Simplify Rational Expression |
37:50 | |
| |
Adding and Subtracting Rational Expressions |
55:04 |
| | |
Intro |
0:00 | |
| | |
Least Common Multiple (LCM) |
0:27 | |
| | |
| Examples: LCM of Numbers |
0:43 | |
| | |
| Example: LCM of Polynomials |
4:02 | |
| | |
Adding and Subtracting |
7:55 | |
| | |
| Least Common Denominator (LCD) |
8:07 | |
| | |
| Example: Numbers |
8:17 | |
| | |
| Example: Rational Expressions |
11:03 | |
| | |
| Equivalent Fractions |
15:22 | |
| | |
Simplifying Complex Fractions |
21:19 | |
| | |
| Example: Previous Lessons |
21:36 | |
| | |
| Example: More Complex |
22:53 | |
| | |
Example 1: Find LCM |
28:30 | |
| | |
Example 2: Add Rational Expressions |
31:44 | |
| | |
Example 3: Subtract Rational Expressions |
39:18 | |
| | |
Example 4: Simplify Rational Expression |
38:26 | |
| |
Graphing Rational Functions |
57:13 |
| | |
Intro |
0:00 | |
| | |
Rational Functions |
0:18 | |
| | |
| Restriction |
0:34 | |
| | |
| Example: Rational Function |
0:51 | |
| | |
Breaks in Continuity |
2:52 | |
| | |
| Example: Continuous Function |
3:10 | |
| | |
| Discontinuities |
3:30 | |
| | |
| Example: Excluded Values |
4:37 | |
| | |
Graphs and Discontinuities |
5:02 | |
| | |
| Common Binomial Factor (Hole) |
5:08 | |
| | |
| Example: Common Factor |
5:31 | |
| | |
| Asymptote |
10:06 | |
| | |
| Example: Vertical Asymptote |
11:08 | |
| | |
Horizontal Asymptotes |
20:00 | |
| | |
| Example: Horizontal Asymptote |
20:25 | |
| | |
Example 1: Holes and Vertical Asymptotes |
26:12 | |
| | |
Example 2: Graph Rational Faction |
28:35 | |
| | |
Example 3: Graph Rational Faction |
39:23 | |
| | |
Example 4: Graph Rational Faction |
47:28 | |
| |
Direct, Joint, and Inverse Variation |
20:21 |
| | |
Intro |
0:00 | |
| | |
Direct Variation |
0:07 | |
| | |
| Constant of Variation |
0:25 | |
| | |
Graph of Constant Variation |
1:26 | |
| | |
| Slope is Constant k |
1:35 | |
| | |
| Example: Straight Lines |
1:41 | |
| | |
Joint Variation |
2:48 | |
| | |
| Three Variables |
2:52 | |
| | |
Inverse Variation |
3:38 | |
| | |
| Rewritten Form |
3:52 | |
| | |
| Examples in Biology |
4:22 | |
| | |
Graph of Inverse Variation |
4:51 | |
| | |
| Asymptotes are Axes |
5:12 | |
| | |
| Example: Inverse Variation |
5:40 | |
| | |
Proportions |
10:11 | |
| | |
| Direct Variation |
10:25 | |
| | |
| Inverse Variation |
11:32 | |
| | |
Example 1: Type of Variation |
12:42 | |
| | |
Example 2: Direct Variation |
14:13 | |
| | |
Example 3: Joint Variation |
16:24 | |
| | |
Example 4: Graph Rational Faction |
18:50 | |
| |
Solving Rational Equations and Inequalities |
55:14 |
| | |
Intro |
0:00 | |
| | |
Rational Equations |
0:15 | |
| | |
| Example: Algebraic Fraction |
0:26 | |
| | |
| Least Common Denominator |
0:49 | |
| | |
| Example: Simple Rational Equation |
1:22 | |
| | |
| Example: Solve Rational Equation |
5:40 | |
| | |
Extraneous Solutions |
9:31 | |
| | |
| Double check |
10:00 | |
| | |
| No Solution |
10:38 | |
| | |
| Example: Extraneous |
10:44 | |
| | |
Rational Inequalities |
14:01 | |
| | |
| Excluded Values |
14:31 | |
| | |
| Solve Related Equation |
14:49 | |
| | |
| Find Intervals |
14:58 | |
| | |
| Use Test Values |
15:25 | |
| | |
| Example: Rational Inequality |
15:51 | |
| | |
| Example: Rational Inequality 2 |
17:07 | |
| | |
Example 1: Rational Equation |
28:50 | |
| | |
Example 2: Rational Equation |
33:51 | |
| | |
Example 3: Rational Equation |
38:19 | |
| | |
Example 4: Rational Inequality |
46:49 | |
| IX. Exponential and Logarithmic Relations |
| |
Exponential Functions |
35:58 |
| | |
Intro |
0:00 | |
| | |
What is an Exponential Function? |
0:12 | |
| | |
| Restriction on b |
0:31 | |
| | |
| Base |
0:46 | |
| | |
| Example: Exponents as Bases |
0:56 | |
| | |
| Variables as Exponents |
1:12 | |
| | |
| Example: Exponential Function |
1:50 | |
| | |
Graphing Exponential Functions |
2:33 | |
| | |
| Example: Using Table |
2:49 | |
| | |
Properties |
11:52 | |
| | |
| Continuous and One to One |
12:00 | |
| | |
| Domain is All Real Numbers |
13:14 | |
| | |
| X-Axis Asymptote |
13:55 | |
| | |
| Y-Intercept |
14:02 | |
| | |
| Reflection Across Y-Axis |
14:31 | |
| | |
Growth and Decay |
15:06 | |
| | |
| Exponential Growth |
15:10 | |
| | |
| Real Life Examples |
15:41 | |
| | |
| Example: Growth |
15:52 | |
| | |
| Example: Decay |
16:12 | |
| | |
| Real Life Examples |
16:30 | |
| | |
Equations |
17:32 | |
| | |
| Bases are Same |
18:05 | |
| | |
| Examples: Variables as Exponents |
18:20 | |
| | |
Inequalities |
21:29 | |
| | |
| Property |
21:51 | |
| | |
| Example: Inequality |
22:37 | |
| | |
Example 1: Graph Exponential Function |
24:05 | |
| | |
Example 2: Growth or Decay |
27:50 | |
| | |
Example 3: Exponential Equation |
29:31 | |
| | |
Example 4: Exponential Inequality |
32:54 | |
| |
Logarithms and Logarithmic Functions |
45:54 |
| | |
Intro |
0:00 | |
| | |
What are Logarithms? |
0:08 | |
| | |
| Restrictions |
0:15 | |
| | |
| Written Form |
0:26 | |
| | |
| Logarithms are Exponents |
0:52 | |
| | |
| Example: Logarithms |
1:49 | |
| | |
Logarithmic Functions |
5:14 | |
| | |
| Same Restrictions |
5:30 | |
| | |
| Inverses |
5:53 | |
| | |
| Example: Logarithmic Function |
6:24 | |
| | |
Graph of the Logarithmic Function |
9:20 | |
| | |
| Example: Using Table |
9:35 | |
| | |
Properties |
15:09 | |
| | |
| Continuous and One to One |
15:14 | |
| | |
| Domain |
15:36 | |
| | |
| Range |
15:56 | |
| | |
| Y-Axis is Asymptote |
16:02 | |
| | |
| X Intercept |
16:12 | |
| | |
Inverse Property |
16:57 | |
| | |
| Compositions of Functions |
17:10 | |
| | |
Equations |
18:30 | |
| | |
| Example: Logarithmic Equation |
19:13 | |
| | |
Inequalities |
20:36 | |
| | |
| Properties |
20:47 | |
| | |
| Example: Logarithmic Inequality |
21:40 | |
| | |
Equations with Logarithms on Both Sides |
24:43 | |
| | |
| Property |
24:51 | |
| | |
| Example: Both Sides |
25:23 | |
| | |
Inequalities with Logarithms on Both Sides |
26:52 | |
| | |
| Property |
27:02 | |
| | |
| Example: Both Sides |
28:05 | |
| | |
Example 1: Solve Log Equation |
31:52 | |
| | |
Example 2: Solve Log Equation |
33:53 | |
| | |
Example 3: Solve Log Equation |
36:15 | |
| | |
Example 4: Solve Log Inequality |
39:19 | |
| |
Properties of Logarithms |
28:43 |
| | |
Intro |
0:00 | |
| | |
Product Property |
0:08 | |
| | |
| Example: Product |
0:46 | |
| | |
Quotient Property |
2:40 | |
| | |
| Example: Quotient |
2:59 | |
| | |
Power Property |
3:51 | |
| | |
| Moved Exponent |
4:07 | |
| | |
| Example: Power |
4:37 | |
| | |
Equations |
5:15 | |
| | |
| Example: Use Properties |
5:58 | |
| | |
Example 1: Simplify Log |
11:17 | |
| | |
Example 2: Single Log |
15:54 | |
| | |
Example 3: Solve Log Equation |
18:48 | |
| | |
Example 4: Solve Log Equation |
22:13 | |
| |
Common Logarithms |
25:23 |
| | |
Intro |
0:00 | |
| | |
What are Common Logarithms? |
0:10 | |
| | |
| Real World Applications |
0:16 | |
| | |
| Base Not Written |
0:27 | |
| | |
| Example: Base 10 |
0:39 | |
| | |
Equations |
1:47 | |
| | |
| Example: Same Base |
1:56 | |
| | |
| Example: Different Base |
2:37 | |
| | |
Inequalities |
6:07 | |
| | |
| Multiplying/Dividing Inequality |
6:21 | |
| | |
| Example: Log Inequality |
6:54 | |
| | |
Change of Base |
12:45 | |
| | |
| Base 10 |
13:24 | |
| | |
| Example: Change of Base |
14:05 | |
| | |
Example 1: Log Equation |
15:21 | |
| | |
Example 2: Common Logs |
17:13 | |
| | |
Example 3: Log Equation |
18:22 | |
| | |
Example 4: Log Inequality |
21:52 | |
| |
Base e and Natural Logarithms |
21:14 |
| | |
Intro |
0:00 | |
| | |
Number e |
0:09 | |
| | |
| Natural Base |
0:21 | |
| | |
| Growth/Decay |
0:33 | |
| | |
| Example: Exponential Function |
0:53 | |
| | |
Natural Logarithms |
1:11 | |
| | |
| ln x |
1:19 | |
| | |
| Inverse and Identity Function |
1:39 | |
| | |
| Example: Inverse Composition |
1:55 | |
| | |
Equations and Inequalities |
4:39 | |
| | |
| Extraneous Solutions |
5:30 | |
| | |
| Examples: Natural Log Equations |
5:48 | |
| | |
Example 1: Natural Log Equation |
9:08 | |
| | |
Example 2: Natural Log Equation |
10:37 | |
| | |
Example 3: Natural Log Inequality |
16:54 | |
| | |
Example 4: Natural Log Inequality |
18:16 | |
| |
Exponential Growth and Decay |
24:30 |
| | |
Intro |
0:00 | |
| | |
Decay |
0:17 | |
| | |
| Decreases by Fixed Percentage |
0:23 | |
| | |
| Rate of Decay |
0:56 | |
| | |
| Example: Finance |
1:34 | |
| | |
Scientific Model of Decay |
3:37 | |
| | |
| Exponential Decay |
3:45 | |
| | |
| Radioactive Decay |
4:13 | |
| | |
| Example: Half Life |
5:33 | |
| | |
Growth |
9:06 | |
| | |
| Increases by Fixed Percentage |
9:18 | |
| | |
| Example: Finance |
10:09 | |
| | |
Scientific Model of Growth |
11:35 | |
| | |
| Population Growth |
12:04 | |
| | |
| Example: Growth |
12:20 | |
| | |
Example 1: Computer Price |
14:00 | |
| | |
Example 2: Stock Price |
15:46 | |
| | |
Example 3: Medicine Disintegration |
19:10 | |
| | |
Example 4: Population Growth |
22:33 | |
| X. Conic Sections |
| |
Midpoint and Distance Formulas |
32:42 |
| | |
Intro |
0:00 | |
| | |
Midpoint Formula |
0:15 | |
| | |
| Example: Midpoint |
0:30 | |
| | |
Distance Formula |
2:30 | |
| | |
| Example: Distance |
2:52 | |
| | |
Example 1: Midpoint and Distance |
4:58 | |
| | |
Example 2: Midpoint and Distance |
8:07 | |
| | |
Example 3: Median Length |
18:51 | |
| | |
Example 4: Perimeter and Area |
23:36 | |
| |
Parabolas |
41:27 |
| | |
Intro |
0:00 | |
| | |
What is a Parabola? |
0:20 | |
| | |
| Definition of a Parabola |
0:29 | |
| | |
| Focus |
0:59 | |
| | |
| Directrix |
1:15 | |
| | |
| Axis of Symmetry |
3:08 | |
| | |
Vertex |
3:33 | |
| | |
| Minimum or Maximum |
3:44 | |
| | |
Standard Form |
4:59 | |
| | |
| Horizontal Parabolas |
5:08 | |
| | |
| Vertex Form |
5:19 | |
| | |
| Upward or Downward |
5:41 | |
| | |
| Example: Standard Form |
6:06 | |
| | |
Graphing Parabolas |
8:31 | |
| | |
| Shifting |
8:51 | |
| | |
| Example: Completing the Square |
9:22 | |
| | |
| Symmetry and Translation |
12:18 | |
| | |
| Example: Graph Parabola |
12:40 | |
| | |
Latus Rectum |
17:13 | |
| | |
| Length |
18:15 | |
| | |
| Example: Latus Rectum |
18:35 | |
| | |
Horizontal Parabolas |
18:57 | |
| | |
| Not Functions |
20:08 | |
| | |
| Example: Horizontal Parabola |
21:21 | |
| | |
Focus and Directrix |
24:11 | |
| | |
| Horizontal |
24:48 | |
| | |
Example 1: Parabola Standard Form |
25:12 | |
| | |
Example 2: Graph Parabola |
30:00 | |
| | |
Example 3: Graph Parabola |
33:13 | |
| | |
Example 4: Parabola Equation |
37:28 | |
| |
Circles |
21:03 |
| | |
Intro |
0:00 | |
| | |
What are Circles? |
0:08 | |
| | |
| Example: Equidistant |
0:17 | |
| | |
| Radius |
0:32 | |
| | |
Equation of a Circle |
0:44 | |
| | |
| Example: Standard Form |
1:11 | |
| | |
Graphing Circles |
1:47 | |
| | |
| Example: Circle |
1:56 | |
| | |
Center Not at Origin |
3:07 | |
| | |
| Example: Completing the Square |
3:51 | |
| | |
Example 1: Equation of Circle |
6:44 | |
| | |
Example 2: Center and Radius |
11:51 | |
| | |
Example 3: Radius |
15:08 | |
| | |
Example 4: Equation of Circle |
16:57 | |
| |
Ellipses |
46:51 |
| | |
Intro |
0:00 | |
| | |
What Are Ellipses? |
0:11 | |
| | |
| Foci |
0:23 | |
| | |
Properties of Ellipses |
1:43 | |
| | |
| Major Axis, Minor Axis |
1:47 | |
| | |
| Center |
1:54 | |
| | |
| Length of Major Axis and Minor Axis |
3:21 | |
| | |
Standard Form |
5:33 | |
| | |
| Example: Standard Form of Ellipse |
6:09 | |
| | |
Vertical Major Axis |
9:14 | |
| | |
| Example: Vertical Major Axis |
9:46 | |
| | |
Graphing Ellipses |
12:51 | |
| | |
| Complete the Square and Symmetry |
13:00 | |
| | |
| Example: Graphing Ellipse |
13:16 | |
| | |
Equation with Center at (h, k) |
19:57 | |
| | |
| Horizontal and Vertical |
20:14 | |
| | |
| Difference |
20:27 | |
| | |
| Example: Center at (h, k) |
20:55 | |
| | |
Example 1: Equation of Ellipse |
24:05 | |
| | |
Example 2: Equation of Ellipse |
27:57 | |
| | |
Example 3: Equation of Ellipse |
32:32 | |
| | |
Example 4: Graph Ellipse |
38:27 | |
| |
Hyperbolas |
38:15 |
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Intro |
0:00 | |
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What are Hyperbolas? |
0:12 | |
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| Two Branches |
0:18 | |
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| Foci |
0:38 | |
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Properties |
2:00 | |
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| Transverse Axis and Conjugate Axis |
2:06 | |
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| Vertices |
2:46 | |
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| Length of Transverse Axis |
3:14 | |
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| Distance Between Foci |
3:31 | |
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| Length of Conjugate Axis |
3:38 | |
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Standard Form |
5:45 | |
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| Vertex Location |
6:36 | |
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| Known Points |
6:52 | |
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Vertical Transverse Axis |
7:26 | |
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| Vertex Location |
7:50 | |
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Asymptotes |
8:36 | |
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| Vertex Location |
8:56 | |
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| Rectangle |
9:28 | |
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| Diagonals |
10:29 | |
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Graphing Hyperbolas |
12:58 | |
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| Example: Hyperbola |
13:16 | |
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Equation with Center at (h, k) |
16:32 | |
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| Example: Center at (h, k) |
17:21 | |
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Example 1: Equation of Hyperbola |
19:20 | |
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Example 2: Equation of Hyperbola |
22:48 | |
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Example 3: Graph Hyperbola |
26:05 | |
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Example 4: Equation of Hyperbola |
36:29 | |
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Conic Sections |
18:43 |
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Intro |
0:00 | |
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Conic Sections |
0:16 | |
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| Double Cone Sections |
0:24 | |
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Standard Form |
1:27 | |
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| General Form |
1:37 | |
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Identify Conic Sections |
2:16 | |
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| B = 0 |
2:50 | |
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| X and Y |
3:22 | |
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Identify Conic Sections, Cont. |
4:46 | |
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| Parabola |
5:17 | |
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| Circle |
5:51 | |
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| Ellipse |
6:31 | |
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| Hyperbola |
7:10 | |
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Example 1: Identify Conic Section |
8:01 | |
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Example 2: Identify Conic Section |
11:03 | |
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Example 3: Identify Conic Section |
11:38 | |
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Example 4: Identify Conic Section |
14:50 | |
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Solving Quadratic Systems |
47:04 |
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Intro |
0:00 | |
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Linear Quadratic Systems |
0:22 | |
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| Example: Linear Quadratic System |
0:45 | |
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Solutions |
2:49 | |
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| Graphs of Possible Solutions |
3:10 | |
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Quadratic Quadratic System |
4:10 | |
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| Example: Elimination |
4:21 | |
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Solutions |
11:39 | |
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| Example: 0, 1, 2, 3, 4 Solutions |
11:50 | |
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Systems of Quadratic Inequalities |
12:48 | |
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| Example: Quadratic Inequality |
13:09 | |
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Example 1: Solve Quadratic System |
21:42 | |
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Example 2: Solve Quadratic System |
29:13 | |
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Example 3: Solve Quadratic System |
35:02 | |
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Example 4: Solve Quadratic Inequality |
40:29 | |
| XI. Sequences and Series |
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Arithmetic Sequences |
21:16 |
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Intro |
0:00 | |
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Sequences |
0:10 | |
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| General Form of Sequence |
0:16 | |
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| Example: Finite/Infinite Sequences |
0:33 | |
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Arithmetic Sequences |
0:28 | |
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| Common Difference |
2:41 | |
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| Example: Arithmetic Sequence |
2:50 | |
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Formula for the nth Term |
3:51 | |
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| Example: nth Term |
4:32 | |
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Equation for the nth Term |
6:37 | |
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| Example: Using Formula |
6:56 | |
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Arithmetic Means |
9:47 | |
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| Example: Arithmetic Means |
10:16 | |
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Example 1: nth Term |
12:38 | |
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Example 2: Arithmetic Means |
13:49 | |
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Example 3: Arithmetic Means |
16:12 | |
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Example 4: nth Term |
18:26 | |
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Arithmetic Series |
21:36 |
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Intro |
0:00 | |
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What are Arithmetic Series? |
0:11 | |
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| Common Difference |
0:28 | |
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| Example: Arithmetic Sequence |
0:43 | |
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| Example: Arithmetic Series |
1:09 | |
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| Finite/Infinite Series |
1:36 | |
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Sum of Arithmetic Series |
2:27 | |
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| Example: Sum |
3:21 | |
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Sigma Notation |
5:53 | |
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| Index |
6:14 | |
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| Example: Sigma Notation |
7:14 | |
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Example 1: First Term |
9:00 | |
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Example 2: Three Terms |
10:52 | |
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Example 3: Sum of Series |
14:14 | |
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Example 4: Sum of Series |
18:13 | |
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Geometric Sequences |
23:03 |
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Intro |
0:00 | |
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Geometric Sequences |
0:11 | |
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| Common Difference |
0:38 | |
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| Common Ratio |
1:08 | |
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| Example: Geometric Sequence |
2:38 | |
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nth Term of a Geometric Sequence |
4:41 | |
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| Example: nth Term |
4:56 | |
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Geometric Means |
6:51 | |
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| Example: Geometric Mean |
7:09 | |
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Example 1: 9th Term |
12:04 | |
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Example 2: Geometric Means |
15:18 | |
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Example 3: nth Term |
18:32 | |
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Example 4: Three Terms |
20:59 | |
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Geometric Series |
22:43 |
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Intro |
0:00 | |
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What are Geometric Series? |
0:11 | |
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| List of Numbers |
0:24 | |
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| Example: Geometric Series |
1:12 | |
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Sum of Geometric Series |
2:16 | |
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| Example: Sum of Geometric Series |
2:41 | |
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Sigma Notation |
4:21 | |
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| Lower Index, Upper Index |
4:38 | |
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| Example: Sigma Notation |
4:57 | |
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Another Sum Formula |
6:08 | |
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| Example: n Unknown |
6:28 | |
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Specific Terms |
7:41 | |
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| Sum Formula |
7:56 | |
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| Example: Specific Term |
8:11 | |
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Example 1: Sum of Geometric Series |
10:02 | |
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Example 2: Sum of 8 Terms |
14:15 | |
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Example 3: Sum of Geometric Series |
18:23 | |
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Example 4: First Term |
20:16 | |
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Infinite Geometric Series |
18:32 |
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Intro |
0:00 | |
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What are Infinite Geometric Series |
0:10 | |
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| Example: Finite |
0:29 | |
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| Example: Infinite |
0:51 | |
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| Partial Sums |
1:09 | |
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| Formula |
1:37 | |
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Sum of an Infinite Geometric Series |
2:39 | |
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| Convergent Series |
2:58 | |
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| Example: Sum of Convergent Series |
3:28 | |
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Sigma Notation |
7:31 | |
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| Example: Sigma |
8:17 | |
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Repeating Decimals |
8:42 | |
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| Example: Repeating Decimal |
8:53 | |
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Example 1: Sum of Infinite Geometric Series |
12:15 | |
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Example 2: Repeating Decimal |
13:24 | |
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Example 3: Sum of Infinite Geometric Series |
15:14 | |
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Example 4: Repeating Decimal |
16:48 | |
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Recursion and Special Sequences |
14:34 |
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Intro |
0:00 | |
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Fibonacci Sequence |
0:05 | |
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| Background of Fibonacci |
0:23 | |
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| Recursive Formula |
0:37 | |
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| Fibonacci Sequence |
0:52 | |
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| Example: Recursive Formula |
2:18 | |
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Iteration |
3:49 | |
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| Example: Iteration |
4:30 | |
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Example 1: Five Terms |
7:08 | |
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Example 2: Three Terms |
9:00 | |
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Example 3: Five Terms |
10:38 | |
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Example 4: Three Iterates |
12:41 | |
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Binomial Theorem |
48:30 |
| | |
Intro |
0:00 | |
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Pascal's Triangle |
0:06 | |
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| Expand Binomial |
0:13 | |
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| Pascal's Triangle |
4:26 | |
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Properties |
6:52 | |
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| Example: Properties of Binomials |
6:58 | |
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Factorials |
9:11 | |
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| Product |
9:28 | |
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| Example: Factorial |
9:45 | |
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Binomial Theorem |
11:08 | |
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| Example: Binomial Theorem |
13:48 | |
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Finding a Specific Term |
18:36 | |
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| Example: Specific Term |
19:26 | |
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Example 1: Expand |
24:39 | |
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Example 2: Fourth Term |
30:26 | |
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Example 3: Five Terms |
36:13 | |
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Example 4: Three Iterates |
45:07 | |