Solving Systems of Equations Using Matrices, Algebra 2

Solving Systems of Equations Using Matrices

IV. Matrices: Lecture 7 | 22:32 min

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Solving Systems of Equations Using Matrices

We can write a system of equations in matrix form. The result is a matrix equation.
A system of equations can be solved using matrices. The solution is the product of the inverse of the matrix of coefficients and the matrix of constants.
The system has a unique solution if and only if the matrix of coefficients has an inverse.
If the matrix of coefficients does not have an inverse, then either there is no solution or there are an infinite number of solutions.

Solving Systems of Equations Using Matrices

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

Intro

Matrix Equations

Example: System of Equations

Solving Systems of Equations

Example 1: Write as Matrix Equation

Example 2: Use Matrix Equations

Example 3: Use Matrix Equations

Example 4: Use Matrix Equations

I. Equations and Inequalities
	Expressions and Formulas	22:23
	Properties of Real Numbers	20:15
	Solving Equations	19:10
	Solving Absolute Value Equations	17:31
	Solving Inequalities	17:14
	Solving Compound and Absolute Value Inequalities	25:00
II. Linear Relations and Functions
	Relations and Functions	32:05
	Linear Equations	14:46
	Slope	23:07
	Writing Linear Functions	23:05
	Special Functions	31:05
	Graphing Inequalities	21:42
III. Systems of Equations and Inequalities
	Solving Systems of Equations by Graphing	17:13
	Solving Systems of Equations Algebraically	23:53
	Solving Systems of Inequalities By Graphing	27:12
	Solving Systems of Equations in Three Variables	28:53
IV. Matrices
	Basic Matrix Concepts	11:34
	Matrix Operations	21:36
	Matrix Multiplication	29:36
	Determinants	33:13
	Cramer's Rule	28:25
	Identity and Inverse Matrices	22:25
	Solving Systems of Equations Using Matrices	22:32
V. Quadratic Functions and Inequalities
	Graphing Quadratic Functions	31:48
	Solving Quadratic Equations by Graphing	27:03
	Solving Quadratic Equations by Factoring	19:53
	Imaginary and Complex Numbers	35:45
	Completing the Square	27:11
	Quadratic Formula and the Discriminant	22:48
	Analyzing the Graphs of Quadratic Functions	30:07
	Graphing and Solving Quadratic Inequalities	27:05
VI. Polynomial Functions
	Properties of Exponents	19:29
	Operations on Polynomials	13:27
	Dividing Polynomials	31:11
	Polynomial Functions	22:30
	Analyzing Graphs of Polynomial Functions	33:29
	Solving Polynomial Functions	21:10
	Remainder and Factor Theorems	31:21
	Roots and Zeros	31:27
	Rational Zero Theorem	31:16
VII. Radical Expressions and Inequalities
	Operations on Functions	34:30
	Inverse Functions and Relations	22:42
	Square Root Functions and Inequalities	30:04
	nth Roots	20:46
	Operations with Radical Expressions	41:11
	Rational Exponents	30:45
	Solving Radical Equations and Inequalities	31:27
VIII. Rational Equations and Inequalities
	Multiplying and Dividing Rational Expressions	40:54
	Adding and Subtracting Rational Expressions	55:04
	Graphing Rational Functions	57:13
	Direct, Joint, and Inverse Variation	20:21
	Solving Rational Equations and Inequalities	55:14
IX. Exponential and Logarithmic Relations
	Exponential Functions	35:58
	Logarithms and Logarithmic Functions	45:54
	Properties of Logarithms	28:43
	Common Logarithms	25:23
	Base e and Natural Logarithms	21:14
	Exponential Growth and Decay	24:30
X. Conic Sections
	Midpoint and Distance Formulas	32:42
	Parabolas	41:27
	Circles	21:03
	Ellipses	46:51
	Hyperbolas	38:15
	Conic Sections	18:43
	Solving Quadratic Systems	47:04
XI. Sequences and Series
	Arithmetic Sequences	21:16
	Arithmetic Series	21:36
	Geometric Sequences	23:03
	Geometric Series	22:43
	Infinite Geometric Series	18:32
	Recursion and Special Sequences	14:34
	Binomial Theorem	48:30

Mathematics: Algebra 2

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
			Add/Subtract Left to Right	3:35
		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
			Addition Property	5:01
			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
			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
			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
		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
	Solving Quadratic Systems			47:04
		Intro		0:00
		Linear Quadratic Systems		0:22
			Example: Linear Quadratic System	0:45
		Solutions		2:49
			Graphs of Possible Solutions	3:10
		Quadratic Quadratic System		4:10
			Example: Elimination	4:21
		Solutions		11:39
			Example: 0, 1, 2, 3, 4 Solutions	11:50
		Systems of Quadratic Inequalities		12:48
			Example: Quadratic Inequality	13:09
		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

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Solving Systems of Equations Using Matrices

Solving Systems of Equations Using Matrices

Mathematics: Algebra 2

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