# Algebra 2 Logarithms and Logarithmic Functions

Section 9: Exponential and Logarithmic Relations: Lecture 2 | 36:31 min

In this lecture you will cover Logarithms and Logarithmic Functions. Our teacher will begin by answering the question What are Logarithms? Then, you will move into Logarithmic Functions, the Graph of the Logarithmic Function, Properties, Inverse Property, and Equations. Then, you will learn how to deal with Logarithms in Inequalities, Equations with Logarithms on Both Sides, and Inequalities with Logarithms on Both Sides.

Professor Fraser

Logarithms and Logarithmic Functions

Slide Duration:Table of Contents

28m 56s

- Intro0:00
- Order of Operations0:51
- Variables and Algebraic Expressions0:57
- Order of Operations3:05
- Monomials5:25
- Examples5:37
- Constant, Coefficient, Degree, Power6:27
- Polynomials8:29
- Examples8:42
- Terms, Like Terms, Binomial, Trinomial8:59
- Formulas12:35
- Examples: Area, Volume, Surface Area12:50
- Lecture Example 115:50
- Lecture Example 221:31
- Additional Example 3-1
- Additional Example 4-2

23m 45s

- Intro0:00
- Real Numbers0:15
- Rational Numbers0:40
- Irrational Numbers1:38
- Venn Diagram of the Real Numbers2:55
- Properties of Real Numbers6:49
- Commutative Property7:06
- Associative Property7:27
- Identity Property8:01
- Inverse Property8:42
- Distributive Property10:05
- Lecture Example 110:43
- Lecture Example 213:08
- Additional Example 3-1
- Additional Example 4-2

24m 41s

- Intro0:00
- Translations0:11
- Example: Verbal to Algebraic Expressions0:44
- Properties of Equality2:51
- Reflexive, Symmetric, Transitive Properties2:58
- Addition, Subtraction, Multiplication, Division3:32
- Solving Equations6:09
- Example6:23
- Solving for a Variable8:49
- Example: Surface Area of a Cone8:58
- Lecture Example 111:06
- Lecture Example 212:39
- Additional Example 3-1
- Additional Example 4-2

17m 36s

- Intro0:00
- Absolute Value Expressions0:10
- Example: Positive Distance0:15
- Absolute Value Equations1:07
- Examples1:18
- No Solutions2:54
- Example: Empty Set2:58
- Number of Solutions3:56
- Examples4:42
- Lecture Example 16:42
- Lecture Example 28:54
- Additional Example 3-1
- Additional Example 4-2

19m 27s

- Intro0:00
- Properties of Inequality0:07
- Addition Property0:21
- Subtraction Property0:48
- Example1:02
- Multiplication Properties1:44
- Multiplying by a Positive Number1:48
- Example: Positive2:17
- Multiplying by a Negative Number2:25
- Example: Negative2:35
- Division Properties3:23
- Example: Positive3:32
- Example: Negative4:04
- Describing the Solution Set6:00
- Set Builder Notation6:15
- Graphing7:15
- Lecture Example 18:04
- Lecture Example 29:09
- Additional Example 3-1
- Additional Example 4-2

24m 8s

- Intro0:00
- Compound Inequalities0:11
- Example0:33
- 'And' Inequality3:41
- Example: Set Intersection4:00
- 'Or' Inequality6:01
- Example: Set Union6:15
- Absolute Value Inequalities8:19
- Examples8:37
- Lecture Example 111:43
- Lecture Example 214:47
- Additional Example 3-1
- Additional Example 4-2

38m 15s

- Intro0:00
- Coordinate Plane0:38
- Example: Origin and Quadrants0:44
- Relations4:08
- Example: Ordered Pairs4:14
- Domain and Range5:05
- Functions5:57
- Example: Mapping6:11
- One-to-One Functions9:58
- Example10:05
- Graphs of Relations13:42
- Example: Discrete and Continuous13:55
- Vertical Line Test16:26
- Examples16:38
- Equations, Relations, Functions19:38
- Example: Independent and Dependent Variables19:45
- Function Notation21:51
- Examples22:27
- Lecture Example 124:39
- Lecture Example 228:29
- Additional Example 3-1
- Additional Example 4-2

12m 50s

- Intro0:00
- Linear Equations and Functions0:12
- Example: Linear Equation0:21
- Example: Linear Function1:16
- Standard Form2:13
- Examples2:43
- Graphing with Intercepts3:26
- Example: Intercepts3:51
- Lecture Example 16:25
- Lecture Example 27:53
- Additional Example 3-1
- Additional Example 4-2

20m 7s

- Intro0:00
- Definition of Slope0:23
- Interpretation of Slope2:19
- Example: 0 Slope and Undefined Slope2:25
- Example: Positive Slope4:04
- Example: Negative Slope4:43
- Parallel Lines6:16
- Perpendicular Lines7:15
- Lecture Example 18:20
- Lecture Example 210:45
- Additional Example 3-1
- Additional Example 4-2

27m 36s

- Intro0:00
- Slope Intercept Form0:08
- Origin of Form0:21
- Example2:08
- Point Slope Form3:47
- Origin of Form4:01
- Parallel and Perpendicular Lines5:36
- Example: Find Parallel Line5:58
- Lecture Example 18:27
- Lecture Example 212:08
- Additional Example 3-1
- Additional Example 4-2

24m 28s

- Intro0:00
- Step Functions0:13
- Graph0:21
- Example: Birthday Function2:32
- Absolute Value Functions5:21
- Graph5:27
- Piecewise Functions7:34
- Example7:38
- Lecture Example 110:20
- Lecture Example 214:38
- Additional Example 3-1
- Additional Example 4-2

30m 37s

- Intro0:00
- Graphing Linear Inequalities0:11
- Example: Linear Inequalities0:20
- Half Plane2:04
- Test Point2:53
- Graphing Absolute Value Inequalities5:38
- Example: Linear Inequalities5:49
- Example: Absolute Value8:23
- Lecture Example 111:39
- Lecture Example 214:50
- Additional Example 3-1
- Additional Example 4-2

21m 27s

- Intro0:00
- Systems of Equations0:14
- Solving by Graphing0:34
- Types of Systems1:07
- Independent (One Solution)2:02
- Dependent (Infinite Solutions)2:30
- Inconsistent (No Solutions, Parallel)3:37
- Lecture Example 14:52
- Lecture Example 28:42
- Additional Example 3-1
- Additional Example 4-2

31m 26s

- Intro0:00
- Solving by Substitution0:15
- Examples0:50
- Solving by Elimination4:19
- Examples4:27
- Solving by Multiplication7:24
- Examples7:37
- Inconsistent and Dependent Systems11:42
- Example: Spotting Differences12:07
- Lecture Example 115:00
- Lecture Example 217:35
- Additional Example 3-1
- Additional Example 4-2

20m 43s

- Intro0:00
- Solving by Graphing0:10
- Example: Single Inequality0:14
- No Solution4:16
- Example: No Solution4:25
- Lecture Example 16:25
- Lecture Example 28:23
- Additional Example 3-1
- Additional Example 4-2

21m 27s

- Intro0:00
- Solving Systems in Three Variables0:15
- Ordered Triple0:36
- Number of Solutions1:32
- Lecture Example 12:19
- Lecture Example 26:14
- Additional Example 3-1
- Additional Example 4-2

14m 8s

- Intro0:00
- What is a Matrix?0:33
- Example: Rectangular Array0:41
- Element1:52
- Examples: More Matrices2:04
- Dimensions3:40
- Examples4:53
- Special Matrices6:31
- (m x 1) Matrix6:36
- Square Matrix7:01
- Zero Matrix7:38
- Equal Matrices8:23
- Examples8:32
- Lecture Example 110:56
- Lecture Example 211:28
- Additional Example 3-1
- Additional Example 4-2

16m 40s

- Intro0:00
- Matrix Addition0:10
- Example1:07
- Matrix Subtraction2:12
- Example2:31
- Scalar Multiplication3:23
- Example4:05
- Properties of Matrix Operations5:31
- Commutative Property5:48
- Associative Property5:59
- Distributive Property6:34
- Lecture Example 17:03
- Lecture Example 28:15
- Additional Example 3-1
- Additional Example 4-2

22m 47s

- Intro0:00
- Dimension Requirement0:19
- Example0:45
- Matrix Multiplication1:35
- Example2:21
- Properties of Matrix Multiplication6:46
- Associative Property6:59
- Distributive Property7:15
- Commutative Property7:39
- Lecture Example 18:49
- Lecture Example 211:43
- Additional Example 3-1
- Additional Example 4-2

25m 47s

- Intro0:00
- What is a Determinant0:15
- Determinant of a 2x2 Matrix0:56
- Difference from Matrices1:16
- Second Order Determinant1:38
- Example2:06
- Determinant of a 3x3 Matrix3:20
- Third Order Determinants3:25
- Origin of Equation (Minors)3:38
- Expansion by Minors6:05
- Example: 3x3 Matrix8:55
- Diagonal Method for 3x3 Matrix12:45
- Example12:55
- Lecture Example 117:03
- Lecture Example 217:42
- Additional Example 3-1
- Additional Example 4-2

25m 42s

- Intro0:00
- System of 2 Equations in 2 Variables0:27
- Example1:20
- System of 3 Equations in 3 Variables3:10
- Example3:51
- Lecture Example 16:45
- Lecture Example 210:22
- Additional Example 3-1
- Additional Example 4-2

27m 1s

- Intro0:00
- Identity Matrix0:10
- Example: 2x2 Matrix2:18
- Matrix Inverses4:40
- Example: Does Not Exist6:04
- Inverse of a 2x2 Matrix8:17
- Example9:38
- Lecture Example 113:19
- Lecture Example 215:57
- Additional Example 3-1
- Additional Example 4-2

28m 40s

- Intro0:00
- Matrix Equations0:22
- Example0:40
- Solving Systems of Equations4:20
- Example5:58
- Lecture Example 19:11
- Lecture Example 215:09
- Additional Example 3-1
- Additional Example 4-2

26m 36s

- Intro0:00
- Quadratic Functions0:10
- Parabola0:50
- Example: Opens Upward1:03
- Example: Opens Downward1:54
- Properties of Parabolas3:17
- Axis of Symmetry3:26
- Vertex4:05
- Example4:28
- Maximum and Minimum Values7:10
- Example: Upwards/Minimum7:32
- Example: Downwards/Maximum8:19
- Lecture Example 19:09
- Lecture Example 213:05
- Additional Example 3-1
- Additional Example 4-2

19m 26s

- Intro0:00
- Quadratic Equations0:18
- Example: Standard Form0:55
- Solving by Graphing1:39
- Roots1:48
- Example: 2 Solutions1:56
- Example: 1 Solution2:39
- Example: 0 Solutions3:10
- Estimating Solutions3:55
- Example4:07
- Lecture Example 15:16
- Lecture Example 27:51
- Additional Example 3-1
- Additional Example 4-2

17m 46s

- Intro0:00
- Factoring Techniques0:16
- Greatest Common Factor (GCF)0:29
- Difference of Two Squares1:45
- Perfect Square Trinomials2:07
- General Trinomials3:16
- Zero Product Rule4:50
- Example5:01
- Lecture Example 16:19
- Lecture Example 28:13
- Additional Example 3-1
- Additional Example 4-2

37m 41s

- Intro0:00
- Properties of Square Roots0:17
- Example: Product and Quotient Rules0:33
- Imaginary Numbers4:04
- Powers of Imaginary Numbers5:06
- Example6:27
- Complex Numbers7:21
- Real and Complex Numbers8:19
- Equality9:04
- Example9:17
- Addition and Subtraction9:43
- Example9:55
- Complex Plane11:38
- Example11:52
- Multiplication13:34
- Example13:43
- Division16:36
- Complex Conjugates16:45
- Example18:16
- Lecture Example 123:40
- Lecture Example 226:34
- Additional Example 3-1
- Additional Example 4-2

16m 42s

- Intro0:00
- Square Root Property0:22
- Examples0:33
- Completing the Square1:48
- Example: Making into Perfect Square1:50
- Solve Equations3:43
- Example3:53
- Equations Where 'a' Not Equal to 16:47
- Example6:57
- Complex Solutions10:14
- Example10:22
- Lecture Example 111:30
- Lecture Example 212:34
- Additional Example 3-1
- Additional Example 4-2

17m 44s

- Intro0:00
- Quadratic Formula0:37
- Example0:56
- One Rational Root3:10
- Why It Works3:26
- Repeated/Double Root3:49
- Complex Solutions4:31
- Example4:50
- Discriminant7:19
- Discriminant Value and Root Type8:50
- Lecture Example 112:08
- Lecture Example 214:15
- Additional Example 3-1
- Additional Example 4-2

23m

- Intro0:00
- Vertex Form0:24
- Example1:56
- Significance of Coefficient 'a'3:15
- Example3:39
- Writing Quadratic Equations in Vertex Form4:51
- Examples5:19
- Lecture Example 18:14
- Lecture Example 210:22
- Additional Example 3-1
- Additional Example 4-2

34m 38s

- Intro0:00
- Graphing Quadratic Inequalities1:14
- Example: Linear Inequality1:29
- Example: Quadratic Inequality3:11
- Solving Quadratic Inequalities6:32
- Example6:38
- Lecture Example 111:50
- Lecture Example 215:09
- Additional Example 3-1
- Additional Example 4-2

20m 28s

- Intro0:00
- Simplifying Exponential Expressions0:32
- Negative Exponents0:54
- Example: Base 01:16
- Examples1:30
- Properties of Exponents2:22
- Base and Exponent2:52
- Lecture Example 18:29
- Lecture Example 210:58
- Additional Example 3-1
- Additional Example 4-2

16m 13s

- Intro0:00
- Adding and Subtracting Polynomials0:24
- Example: Signs0:34
- Multiplying Polynomials3:04
- Example3:12
- Lecture Example 16:40
- Lecture Example 27:21
- Additional Example 3-1
- Additional Example 4-2

29m 26s

- Intro0:00
- Dividing by a Monomial0:16
- Example0:28
- Long Division3:24
- Example: Missing Terms, Remainder3:49
- Example: Long Division6:51
- Synthetic Division10:13
- Example10:44
- Divisor in Synthetic Division13:18
- Example: Coefficient Not 113:30
- Lecture Example 116:41
- Lecture Example 218:22
- Additional Example 3-1
- Additional Example 4-2

29m 34s

- Intro0:00
- Polynomial in One Variable0:17
- Degree n0:30
- Descending Order0:43
- Example: Leading Coefficient1:04
- Function Values3:31
- Example3:42
- Zeros of Polynomial Functions5:45
- Example: Zeros6:04
- End Behavior9:51
- Example: 4 Situations10:51
- Lecture Example 117:30
- Lecture Example 219:11
- Additional Example 3-1
- Additional Example 4-2

34m 36s

- Intro0:00
- Graphing Polynomial Functions0:09
- End Behavior0:19
- Examples: Degree and Sign of Polynomials1:13
- Location Principle4:50
- Example6:19
- Maximum and Minimum Points7:34
- Example: Relative Maximum and Relative Minimum7:44
- Lecture Example 110:17
- Lecture Example 215:13
- Additional Example 3-1
- Additional Example 4-2

19m 23s

- Intro0:00
- Factoring Polynomials0:08
- Example: Greatest Common Factor (GCF)0:40
- Example: Perfect Square Trinomials1:30
- Example: General Trinomials2:48
- Sum and Difference of Two Cubes3:25
- Example4:18
- Quadratic Form6:20
- Lecture Example 17:30
- Lecture Example 210:43
- Additional Example 3-1
- Additional Example 4-2

27m 52s

- Intro0:00
- Remainder Theorem0:04
- Quotient and Remainder0:30
- Examples1:34
- Synthetic Substitution5:04
- Example5:28
- Factor Theorem10:00
- Factoring Polynomials11:21
- Example11:51
- Lecture Example 116:38
- Lecture Example 218:41
- Additional Example 3-1
- Additional Example 4-2

31m 4s

- Intro0:00
- Numbers of Roots0:10
- Example: Real and Complex Roots0:23
- Descartes' Rule of Signs3:43
- Example: Positive Real Roots4:58
- Example: Negative Real Roots8:00
- Finding the Roots12:11
- Conjugate Roots13:24
- Lecture Example 115:41
- Lecture Example 219:41
- Additional Example 3-1
- Additional Example 4-2

29m 27s

- Intro0:00
- Equation0:14
- Leading Coefficient and Constant Term0:30
- Example2:15
- Leading Coefficient Equal to 18:08
- Example9:20
- Finding Rational Zeros11:48
- Lecture Example 112:10
- Lecture Example 215:59
- Additional Example 3-1
- Additional Example 4-2

35m 12s

- Intro0:00
- Arithmetic Operations0:12
- Example: Domain0:25
- Composition of Functions7:35
- Example7:55
- Composition is Not Commutative17:13
- Example18:18
- Lecture Example 121:51
- Lecture Example 224:25
- Additional Example 3-1
- Additional Example 4-2

18m 12s

- Intro0:00
- Inverse of a Relation0:24
- Example: Ordered Pairs0:33
- Inverse of a Function2:15
- Procedure to Construct an Inverse Function4:28
- Example: Inverse Function4:58
- Example: Inverse Function 27:31
- Inverses and Compositions8:41
- Lecture Example 19:59
- Lecture Example 210:45
- Additional Example 3-1
- Additional Example 4-2

26m 24s

- Intro0:00
- Square Root Functions0:06
- Example: Not Square Root Function0:23
- Example: Square Root Function1:17
- Graphing Square Root Functions3:11
- Example: Radicand3:21
- Square Root Inequalities6:51
- Example7:13
- Lecture Example 111:27
- Lecture Example 214:05
- Additional Example 3-1
- Additional Example 4-2

24m 6s

- Intro0:00
- Definition of the nth Root0:13
- Example0:36
- Principal nth Root2:18
- Index3:04
- Examples3:20
- Using Absolute Values6:25
- Examples6:52
- Lecture Example 111:26
- Lecture Example 213:17
- Additional Example 3-1
- Additional Example 4-2

34m 38s

- Intro0:00
- Properties of Radicals0:22
- Example1:37
- Simplifying Radical Expressions2:58
- Examples3:24
- Rationalizing Denominators4:08
- Examples4:18
- Conjugate Radical Expressions8:01
- Example8:09
- Adding and Subtracting Radicals11:23
- Examples11:44
- Multiplying Radicals12:57
- Examples13:03
- Lecture Example 116:53
- Lecture Example 220:11
- Additional Example 3-1
- Additional Example 4-2

24m 36s

- Intro0:00
- Definition 10:24
- nth Root0:44
- Example: Even1:29
- Definition 22:55
- Simplifying Expressions3:20
- Examples3:40
- Simplified Form7:07
- Example7:32
- Lecture Example 18:18
- Lecture Example 210:20
- Additional Example 3-1
- Additional Example 4-2

38m 46s

- Intro0:00
- Radical Equations0:23
- Examples0:34
- Example: Radical Equation4:47
- Extraneous Roots12:29
- Eliminating nth Roots14:28
- Examples14:54
- Radical Inequalities16:38
- Example17:18
- Lecture Example 120:28
- Lecture Example 222:57
- Additional Example 3-1
- Additional Example 4-2

30m 11s

- Intro0:00
- Simplifying Rational Expressions0:12
- Examples: Rational Expressions0:31
- Factoring -13:26
- Example3:33
- Multiplying and Dividing Rational Expressions4:50
- Multiplying5:08
- Dividing5:16
- Example6:10
- Factoring9:13
- Example9:33
- Complex Fractions13:15
- Example13:27
- Lecture Example 115:36
- Lecture Example 218:25
- Additional Example 3-1
- Additional Example 4-2

51m 53s

- Intro0:00
- Example: Fractions0:22
- Least Common Multiple (LCM)1:36
- Example2:07
- Adding and Subtracting7:56
- Least Common Denominator (LCD)8:01
- Example: Fractions8:14
- Example: Rational Expression10:23
- Equivalent Fractions13:45
- Example14:20
- Simplifying Complex Fractions20:03
- Example20:28
- Lecture Example 126:34
- Lecture Example 231:06
- Additional Example 3-1
- Additional Example 4-2

45m 13s

- Intro0:00
- Rational Functions0:35
- Example0:57
- Breaks in Continuity2:48
- Discontinuities3:19
- Example: Excluded Values3:52
- Graphs and Discontinuities4:36
- Example: Hole Discontinuity6:07
- Example: Asymptote8:53
- Horizontal Asymptotes13:34
- Example13:54
- Lecture Example 117:58
- Lecture Example 220:29
- Additional Example 3-1
- Additional Example 4-2

21m 49s

- Intro0:00
- Direct Variation0:16
- Constant of Variation0:44
- Graph of Direct Variation1:28
- Example: Straight Line1:36
- Joint Variation2:55
- Inverse Variation4:17
- Example4:50
- Graph of Inverse Variation5:35
- Example6:00
- Proportions8:00
- Example9:28
- Lecture Example 112:32
- Lecture Example 214:26
- Additional Example 3-1
- Additional Example 4-2

53m 21s

- Intro0:00
- Rational Equations0:15
- Example: Not Rational Equation0:26
- Example: X in Denominator0:38
- Example: LCD1:08
- Example: Rational Equations5:19
- Extraneous Solutions12:08
- Example12:42
- Rational Inequalities15:31
- Example15:45
- Example: Rational Inequalities12:05
- Lecture Example 132:06
- Lecture Example 235:18
- Additional Example 3-1
- Additional Example 4-2

28m 22s

- Intro0:00
- What is an Exponential Function?0:11
- Exponent and Base0:38
- Graphing Exponential Functions1:31
- Example1:34
- Properties4:05
- Growth and Decay9:38
- Equations10:32
- Example11:05
- Inequalities13:00
- Example14:29
- Lecture Example 116:48
- Lecture Example 218:50
- Additional Example 3-1
- Additional Example 4-2

36m 31s

- Intro0:00
- What are Logarithms?0:17
- Examples1:30
- Logarithmic Functions4:09
- Graph of the Logarithmic Function4:52
- Properties9:08
- Inverse Property10:47
- Equations11:44
- Example12:11
- Inequalities14:45
- Equations with Logarithms on Both Sides17:00
- Example17:18
- Inequalities with Logarithms on Both Sides19:17
- Example19:32
- Lecture Example 120:31
- Lecture Example 222:38
- Additional Example 3-1
- Additional Example 4-2

29m 50s

- Intro0:00
- Product Property0:08
- Example0:26
- Quotient Property1:06
- Example1:12
- Power Rule3:29
- Example3:33
- Equations5:43
- Example6:19
- Lecture Example 112:19
- Lecture Example 216:13
- Additional Example 3-1
- Additional Example 4-2

27m 10s

- Intro0:00
- What are Common Logarithms?0:54
- Base 100:58
- Equations2:00
- Examples2:22
- Inequalities5:35
- Example5:42
- Change of Base9:23
- Example10:09
- Lecture Example 112:04
- Lecture Example 215:16
- Additional Example 3-1
- Additional Example 4-2

19m 52s

- Intro0:00
- The Number 'e'0:32
- Natural Base0:44
- Euler1:12
- Natural Exponential Function1:38
- Natural Log Function2:44
- Growth and Decay2:55
- Natural Logarithms3:16
- Graph (Inverse)3:34
- Equations and Inequalities4:49
- Lecture Example 17:21
- Lecture Example 29:10
- Additional Example 3-1
- Additional Example 4-2

28m 10s

- Intro0:00
- Decay0:15
- Fixed Percentage0:24
- Rate of Decay2:35
- Scientific Model of Decay (Exponential Decay)4:17
- Graph5:19
- Growth6:19
- Rate of Growth6:36
- Scientific Model of Growth (Exponential Growth)6:41
- Graph6:48
- Lecture Example 17:48
- Additional Example 3-1
- Additional Example 4-2

29m 35s

- Intro0:00
- Midpoint Formula0:35
- Distance Formula1:42
- Example2:52
- Lecture Example 13:40
- Lecture Example 26:37
- Additional Example 3-1
- Additional Example 4-2

26m 11s

- Intro0:00
- What is a Parabola?0:21
- Focus and Directrix0:33
- Axis of Symmetry1:41
- Vertex2:03
- Example2:15
- Standard Form3:11
- Upward and Downward4:07
- Graphing Parabolas5:24
- Example6:32
- Latus Rectum7:37
- Horizontal Parabolas9:10
- Focus and Direction12:31
- Lecture Example 113:11
- Lecture Example 216:46
- Additional Example 3-1
- Additional Example 4-2

17m 33s

- Intro0:00
- What are Circles0:17
- Center, Radius0:37
- Equation (Standard Form)0:46
- Graphing1:21
- Center Not at Origin1:53
- Example2:06
- Lecture Example 14:16
- Lecture Example 28:22
- Additional Example 3-1
- Additional Example 4-2

38m 57s

- Intro0:00
- What are Ellipses?0:59
- Foci1:04
- Properties3:47
- Major Axis, Minor Axis4:03
- Standard Form7:22
- Example8:05
- Vertical Major Axis10:12
- Example10:40
- Graphing Ellipses13:33
- Example: Completing the Square14:04
- Equation with Center at (h,k)17:25
- Example17:53
- Lecture Example 119:36
- Lecture Example 223:52
- Additional Example 3-1
- Additional Example 4-2

37m 59s

- Intro0:00
- What are Hyperbolas?1:09
- Properties2:35
- Transverse Axis, Conjugate Axis2:57
- Center, Vertices3:54
- Standard Form4:33
- Vertical Transverse Axis6:35
- Asymptotes10:17
- Graphing Hyperbolas13:44
- Example17:23
- Equation with Center at (h,k)18:20
- Lecture Example 120:19
- Lecture Example 223:25
- Additional Example 3-1
- Additional Example 4-2

23m 10s

- Intro0:00
- What are Conic Sections?2:16
- Standard Form2:58
- Example5:29
- Identifying Conic Sections6:14
- Example6:55
- Lecture Example 18:55
- Lecture Example 211:18
- Additional Example 3-1
- Additional Example 4-2

28m 18s

- Intro0:00
- Linear Quadratic Systems0:04
- Example0:28
- Solutions3:13
- Quadratic Quadratic System3:36
- Example: Elimination3:45
- Solutions7:34
- Systems of Quadratic Inequalities7:55
- Example8:07
- Lecture Example 111:10
- Lecture Example 216:12
- Additional Example 3-1
- Additional Example 4-2

27m 44s

- Intro0:00
- Sequences0:27
- Example: Term0:36
- Arithmetic Sequence2:13
- Common Difference2:22
- Example2:35
- Formula for nth Term3:39
- Example4:29
- Equation for nth Term5:58
- Example6:10
- Arithmetic Means7:40
- Example8:13
- Lecture Example 114:08
- Lecture Example 215:35
- Additional Example 3-1
- Additional Example 4-2

29m 12s

- Intro0:00
- What are Arithmetic Series?0:22
- Example: Sequence0:29
- Example: Common Difference (d)0:35
- Sum of Arithmetic Series2:52
- Example3:44
- Sigma Notation6:10
- Example6:48
- Lecture Example 18:32
- Lecture Example 212:39
- Additional Example 3-1
- Additional Example 4-2

24m 52s

- Intro0:00
- What are Geometric Sequences?0:20
- Common Ratio1:03
- Example1:20
- nth Term of a Geometric Sequence3:39
- Geometric Means4:16
- Example: Missing Term5:06
- Lecture Example 18:09
- Lecture Example 211:42
- Additional Example 3-1
- Additional Example 4-2

27m 2s

- Intro0:00
- What are Geometric Series?0:20
- Example: Common Ratio1:00
- Sum of Geometric Series2:27
- Example4:01
- Sigma Notation4:56
- Example: Index5:24
- Example6:20
- Another Sum Formula7:51
- Specific Terms9:19
- Lecture Example 111:15
- Lecture Example 214:30
- Additional Example 3-1
- Additional Example 4-2

24m 1s

- Intro0:00
- What are Infinite Geometric Series?0:35
- Partial Sums of the Infinite Series1:17
- Example1:24
- Sum of an Infinite Geometric Series3:16
- Convergent Series3:25
- Example4:17
- Sigma Notation5:31
- Example5:43
- Repeating Decimals6:38
- Example6:48
- Lecture Example 19:33
- Lecture Example 211:20
- Additional Example 3-1
- Additional Example 4-2

17m 11s

- Intro0:00
- Fibonacci Sequence0:17
- Example: Fibonacci Sequence0:36
- Example: Recursive Formula2:38
- Iteration3:40
- Example4:57
- Lecture Example 17:10
- Lecture Example 29:03
- Additional Example 3-1
- Additional Example 4-2

38m 25s

- Intro0:00
- Pascal's Triangle0:11
- General Form2:43
- Properties7:01
- Binomial Theorem9:20
- Example11:47
- Finding a Specific Term16:24
- Example16:32
- Lecture Example 120:35
- Lecture Example 223:30
- Additional Example 3-1
- Additional Example 4-2

19m 53s

- Intro0:00
- Math Induction Principle0:19
- Example0:29
- Counter Examples5:00
- Example5:14
- Lecture Example 17:16
- Lecture Example 210:53
- Additional Example 3-1
- Additional Example 4-2

For more information, please see full course syllabus of Algebra 2

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