INSTRUCTORS Carleen Eaton Grant Fraser

Join Dr. Carleen Eaton’s Algebra 2 online class with clear explanations and tons of step-by-step examples of commonly seen problems. Dr. Eaton utilizes her 15+ years teaching experience to bring insight and problem-solving strategies to help you ace your home and class.

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## 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
Multiply/Divide Left to Right 2:55
Monomials 4:40
Examples of Monomials 4:52
Constant 5:27
Coefficient 5:46
Degree 6:25
Power 7:15
Polynomials 8:02
Examples of Polynomials 8:24
Binomials, Trinomials, Monomials 8:53
Term 9:21
Like Terms 10:02
Formulas 11:00
Example: Pythagorean Theorem 11:15
Example 1: Evaluate the Algebraic Expression 11:50
Example 2: Evaluate the Algebraic Expression 14:38
Example 3: Area of a Triangle 19:11
Example 4: Fahrenheit to Celsius 20:41
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
Real Number System 5:27
Natural Numbers 5:32
Whole Numbers 5:53
Integers 6:19
Fractions 6:46
Properties of Real Numbers 7:15
Commutative Property 7:34
Associative Property 8:07
Identity Property 9:04
Inverse Property 9:53
Distributive Property 11:03
Example 1: What Set of Numbers? 12:21
Example 2: What Properties Are Used? 13:56
Example 3: Multiplicative Inverse 16:00
Example 4: Simplify Using Properties 17:18
Solving Equations 19:10
Intro 0:00
Translations 0:06
Verbal Expressions and Algebraic Expressions 0:13
Example: Sum of Two Numbers 0:19
Example: Square of a Number 1:33
Properties of Equality 3:20
Reflexive Property 3:30
Symmetric Property 3:42
Transitive Property 4:01
Subtraction Property 5:37
Multiplication Property 6:02
Division Property 6:30
Solving Equations 6:58
Example: Using Properties 7:18
Solving for a Variable 8:25
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
Example 4: Simplify Using Properties 17:26
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
Solving Inequalities 17:14
Intro 0:00
Properties of Inequalities 0:08
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
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
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
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
Same Dimensions 0:25
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 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

Intro 0:00
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
Standard Form 0:18
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
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
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
Standard Form 0:29
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 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
Test Point 0:18
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
Like Terms and Like Monomials 0:23
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
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
Odd Degrees 12:51
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
Example 1: Factor Polynomial 12:03
Example 2: Factor Polynomial 13:54
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
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
Intro 0:00
Quotient Property 0:29
Example: Quotient 1:00
Example: Product Property 1:47
Rationalizing Denominators 8:27
Conjugates 12:07
Distributive Property 19:10
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
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
Restriction: Index is Even 11:53
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
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
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
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
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
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
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
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 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
Intro 0:00
What are Hyperbolas? 0:12
Two Branches 0:18
Foci 0:38
Properties 2:00
Transverse Axis and Conjugate Axis 2:06
Vertices 2:46
Length of Transverse Axis 3:14
Distance Between Foci 3:31
Length of Conjugate Axis 3:38
Standard Form 5:45
Vertex Location 6:36
Known Points 6:52
Vertical Transverse Axis 7:26
Vertex Location 7:50
Asymptotes 8:36
Vertex Location 8:56
Rectangle 9:28
Diagonals 10:29
Graphing Hyperbolas 12:58
Example: Hyperbola 13:16
Equation with Center at (h, k) 16:32
Example: Center at (h, k) 17:21
Example 1: Equation of Hyperbola 19:20
Example 2: Equation of Hyperbola 22:48
Example 3: Graph Hyperbola 26:05
Example 4: Equation of Hyperbola 36:29
Conic Sections 18:43
Intro 0:00
Conic Sections 0:16
Double Cone Sections 0:24
Standard Form 1:27
General Form 1:37
Identify Conic Sections 2:16
B = 0 2:50
X and Y 3:22
Identify Conic Sections, Cont. 4:46
Parabola 5:17
Circle 5:51
Ellipse 6:31
Hyperbola 7:10
Example 1: Identify Conic Section 8:01
Example 2: Identify Conic Section 11:03
Example 3: Identify Conic Section 11:38
Example 4: Identify Conic Section 14:50
Intro 0:00
Solutions 2:49
Graphs of Possible Solutions 3:10
Example: Elimination 4:21
Solutions 11:39
Example: 0, 1, 2, 3, 4 Solutions 11:50
Example 1: Solve Quadratic System 21:42
Example 2: Solve Quadratic System 29:13
Example 3: Solve Quadratic System 35:02
Example 4: Solve Quadratic Inequality 40:29

## XI. Sequences and Series

Arithmetic Sequences 21:16
Intro 0:00
Sequences 0:10
General Form of Sequence 0:16
Example: Finite/Infinite Sequences 0:33
Arithmetic Sequences 0:28
Common Difference 2:41
Example: Arithmetic Sequence 2:50
Formula for the nth Term 3:51
Example: nth Term 4:32
Equation for the nth Term 6:37
Example: Using Formula 6:56
Arithmetic Means 9:47
Example: Arithmetic Means 10:16
Example 1: nth Term 12:38
Example 2: Arithmetic Means 13:49
Example 3: Arithmetic Means 16:12
Example 4: nth Term 18:26
Arithmetic Series 21:36
Intro 0:00
What are Arithmetic Series? 0:11
Common Difference 0:28
Example: Arithmetic Sequence 0:43
Example: Arithmetic Series 1:09
Finite/Infinite Series 1:36
Sum of Arithmetic Series 2:27
Example: Sum 3:21
Sigma Notation 5:53
Index 6:14
Example: Sigma Notation 7:14
Example 1: First Term 9:00
Example 2: Three Terms 10:52
Example 3: Sum of Series 14:14
Example 4: Sum of Series 18:13
Geometric Sequences 23:03
Intro 0:00
Geometric Sequences 0:11
Common Difference 0:38
Common Ratio 1:08
Example: Geometric Sequence 2:38
nth Term of a Geometric Sequence 4:41
Example: nth Term 4:56
Geometric Means 6:51
Example: Geometric Mean 7:09
Example 1: 9th Term 12:04
Example 2: Geometric Means 15:18
Example 3: nth Term 18:32
Example 4: Three Terms 20:59
Geometric Series 22:43
Intro 0:00
What are Geometric Series? 0:11
List of Numbers 0:24
Example: Geometric Series 1:12
Sum of Geometric Series 2:16
Example: Sum of Geometric Series 2:41
Sigma Notation 4:21
Lower Index, Upper Index 4:38
Example: Sigma Notation 4:57
Another Sum Formula 6:08
Example: n Unknown 6:28
Specific Terms 7:41
Sum Formula 7:56
Example: Specific Term 8:11
Example 1: Sum of Geometric Series 10:02
Example 2: Sum of 8 Terms 14:15
Example 3: Sum of Geometric Series 18:23
Example 4: First Term 20:16
Infinite Geometric Series 18:32
Intro 0:00
What are Infinite Geometric Series 0:10
Example: Finite 0:29
Example: Infinite 0:51
Partial Sums 1:09
Formula 1:37
Sum of an Infinite Geometric Series 2:39
Convergent Series 2:58
Example: Sum of Convergent Series 3:28
Sigma Notation 7:31
Example: Sigma 8:17
Repeating Decimals 8:42
Example: Repeating Decimal 8:53
Example 1: Sum of Infinite Geometric Series 12:15
Example 2: Repeating Decimal 13:24
Example 3: Sum of Infinite Geometric Series 15:14
Example 4: Repeating Decimal 16:48
Recursion and Special Sequences 14:34
Intro 0:00
Fibonacci Sequence 0:05
Background of Fibonacci 0:23
Recursive Formula 0:37
Fibonacci Sequence 0:52
Example: Recursive Formula 2:18
Iteration 3:49
Example: Iteration 4:30
Example 1: Five Terms 7:08
Example 2: Three Terms 9:00
Example 3: Five Terms 10:38
Example 4: Three Iterates 12:41
Binomial Theorem 48:30
Intro 0:00
Pascal's Triangle 0:06
Expand Binomial 0:13
Pascal's Triangle 4:26
Properties 6:52
Example: Properties of Binomials 6:58
Factorials 9:11
Product 9:28
Example: Factorial 9:45
Binomial Theorem 11:08
Example: Binomial Theorem 13:48
Finding a Specific Term 18:36
Example: Specific Term 19:26
Example 1: Expand 24:39
Example 2: Fourth Term 30:26
Example 3: Five Terms 36:13
Example 4: Three Iterates 45:07

## Course Details:

Duration: 34 hours, 11 minutes

Number of Lessons: 72

This online course is essential for both high school and college students taking Algebra or studying for a standardized test, and meets or exceeds most mathematics standards. Algebra sets the foundation for progressing into further courses such as Precalculus and Calculus, and Dr. Eaton makes it easy to understand.

• Free Sample Lessons
• Closed Captioning (CC)
• Practice Questions
• Study Guides

Topics Include:

• Properties of Real Numbers
• Linear Equations
• Systems of Equations
• Matrices
• Polynomial Functions
• Rational Expressions
• Exponential & Logarithmic Relations
• Conic Sections
• Sequences & Series

Dr. Carleen Eaton has an M.D. from the UCLA School of Medicine and has won numerous "Teacher of the Year" awards in her 15+ year career. She is also continually ranked as one of the top instructors in California.

### Student Testimonials:

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"Dr. Eaton is really OUTSTANDING!" — Guillermo M.

"Great teaching style, way better than my teacher. I like the step by step explanations and examples." — Mohammad J.

“Your demonstration was impeccable! I have chosen certain lectures from you in preparation for my GRE's to enter Temple University! Thanks! This was much better than that boring GRE manual!” — Lee F.