Solving Equations by Graphing, Algebra 1

Solving Equations by Graphing

IX. Quadratic Functions: Lecture 2 | 40:42 min

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Solving Equations by Graphing

A quadratic equation is one that can be written in the form ax² + bx + c = 0, where a ≠ 0. Its solutions are called the roots of the equation.
The roots of a quadratic equation are x-intercepts of the graph of the related quadratic function.
A quadratic equation has 2 real roots if its graph has two x-intercepts, 1 real root if it has one x-intercept (in this case, the graph is tangent to the x axis and the root is called a double root), and no real roots if it has no x-intercepts.
If a root is not an integer, estimate the root by stating the two consecutive integers it lies between.
In general, use graphing to solve an equation only if you would be satisfied with an estimate for the solutions, not exact values.
A real number is a zero of the quadratic function f(x) if and only if it is a root of the equation f(x) = 0.

Solving Equations by Graphing

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

Solving a Quadratic Equation

Example

Two Distinct Solutions/Roots

One Double Root

Example: One X-Intercept

No Real Roots

Example

Estimating Solutions

Example: Not Integers

Example 1: Solve by Graphing

Example 2: Solve by Graphing

Example 3: Solve by Graphing

Example 4: Estimate by Graphing

I. Basic Concepts
	Variables and Expressions	11:22
	Order of Operations	15:59
	Distributive Property	9:50
	Real Number System	17:58
	Functions and Graphs	34:39
II. Solving Linear Equations
	From Sentences to Equations	16:05
	Addition and Subtraction Techniques	15:24
	Multiplication and Division Techniques	15:41
	Techniques for Multistep Equations	14:31
	When the Variable is on Both Sides of the Equation	20:17
	Ratios and Proportion	16:05
	Applications of Percents	13:46
	More Than One Variable	20:38
III. Functions
	Relations	16:58
	Functions	19:27
	Linear Functions	20:15
IV. Linear Functions and Their Graphs
	Slope and Rate of Change	19:46
	Direct Variation	13:54
	Slope Intercept Form of an Equation	12:06
	Point Slope Form of an Equation	9:07
	Parallel Lines and Perpendicular Lines	18:02
V. Systems of Equations
	Graphing Systems of Equations	22:45
	Solving by Substituting	22:41
	Solving by Addition and Subtraction	16:13
VI. Inequalities
	Addition & Subtraction Techniques	11:34
	Multiplication & Division Techniques	10:49
	Techniques for Multistep Inequalities	16:56
	Compound Inequalities	21:32
	Equations with Absolute Value	24:16
	Inequalities with Absolute Values	17:37
	Graphing Inequalities with Two Variables	24:33
	Graphing Systems of Inequalities	24:04
VII. Polynomials
	Multiplying Monomials	22:19
	Dividing Monomials	24:02
	Polynomials	8:56
	Adding and Subtracting Polynomials	15:51
	Multiplying Polynomials by Monomials	18:17
	Multiplying Polynomials	18:02
	Special Products	17:00
VIII. Factoring
	Special Product	17:51
	Factoring Using Greatest Common Factor	25:21
	Factoring Trinomials with Leading Coefficient of 1	27:11
	Factoring General Trinomials	46:09
	Factoring the Difference of Two Squares	24:03
	Factoring Perfect Squares	18:10
IX. Quadratic Functions
	Graphing Quadratic Functions	35:45
	Solving Equations by Graphing	40:42
	Solving Equations by Completing the Square	28:13
	Solving Equations Using the Quadratic Formula	17:17
X. Radical Expressions and Equations
	Simplifying Radical Expressions	41:30
	Operations with Radical Expressions	21:52
	Solving Radical Equations	27:00
	Pythagorean Theorem	17:24
	Distance Formula	26:50
XI. Rational Expressions and Equations
	Inverse Variation	24:13
	Rational Expressions	34:22
	Multiplying Rational Expressions	22:58
	Dividing Rational Expressions	21:49
	Dividing Polynomials	35:57
	Adding and Subtracting Rational Expressions with Like Denominators	17:38
	Adding and Subtracting Rational Expressions with Unlike Denominators	37:16
	Complex Fractions	25:38
	Rational Equations	38:09

Mathematics: Algebra 1

I. Basic Concepts
	Variables and Expressions			11:22
		Intro		0:00
			History of Algebra	0:12
			Origin of Word	0:21
			Real World Problems	0:35
		Definitions		0:58
			Variable	1:03
			Algebraic Expression	1:37
			Operations	2:02
		Example 1: Words into Expressions		3:02
		Example 2: Words into Expressions		5:20
		Example 3: Words into Expressions		6:45
		Example 4: Words into Expressions		9:46
	Order of Operations			15:59
		Intro		0:00
			Example	0:17
			Definition	0:57
		Procedure to Evaluate an Arithmetic Expression		1:08
			Grouping Symbols (Parentheses, Brackets, Braces)	1:19
			Powers	1:42
			Multiply/Divide Left to Right	1:57
			Add/Subtract Left to Right	2:21
			Example: Fraction Bar	2:49
		Example 1: Evaluate Arithmetic Expression		3:45
		Example 2: Evaluate Arithmetic Expression		7:28
		Example 3: Evaluate Arithmetic Expression		10:11
		Example 4: Evaluate with Variables		13:12
	Distributive Property			9:50
		Intro		0:00
		Distributive Property Statements		0:23
			Moving Forward	0:49
			Rule for Subtraction	1:14
			Reverse Order	1:40
			Several Numbers	2:17
		Example 1: Evaluate Using Distributive Property		2:56
		Example 2: Multiply Using Distributive Property		4:10
		Example 3: Simplify Using Distributive Property		4:59
		Example 4: Simplify Using Distributive Property		7:03
	Real Number System			17:58
		Intro		0:00
		Real Number System		0:31
			Natural Numbers	0:39
			Whole Numbers	1:11
			Integers	1:23
			Rational Numbers	1:52
			Cannot Divide by Zero	2:18
			Decimals	2:27
			Example: Terminating or Repeating	2:39
		Real Number System, Cont.		3:37
			Square Roots	3:42
			Examples	3:54
			Irrational Numbers	4:36
			Examples	5:02
			Perfect Square	5:54
		Real Number System, Cont.		6:49
			Example: Number Line	7:02
		Example 1: Which Set of Numbers		7:54
		Example 2: Graph on Number Line		10:04
		Example 3: Approximate Irrational Number		12:47
		Example 4: Order Largest to Smallest		13:57
	Functions and Graphs			34:39
		Intro		0:00
		Functions		0:15
			Example: Function	0:29
			Example: Not Functions (Relations)	1:15
		Graphs		4:44
			Visual Display	4:53
			Example: X and Y	5:03
			Coordinate Pairs	5:53
			Discrete Function	8:19
			Continuous Function	8:55
		Vertical Line Test		10:55
			Test if Function	11:12
			Example: Pass Through Points	11:43
		Domain and Range		14:13
			Example	14:43
		Example 1: Function Given by Table		16:24
		Example 2: Cost of Gas		18:46
		Example 3: Cost of Gas		23:15
		Example 4: Cost of Mail		29:07
II. Solving Linear Equations
	From Sentences to Equations			16:05
		Intro		0:00
			Real World Applications	0:18
		Strategy		0:26
			Using Variables	0:32
			Translate Phrases	0:48
			Identity Equality Words	1:07
		Example 1: Write Equation		1:32
		Example 2: Write Equation		4:14
		Example 3: Sisters' Ages		8:26
		Example 4: Surface Area of Cylinder		12:52
	Addition and Subtraction Techniques			15:24
		Intro		0:00
		Techniques		0:21
			Addition Principle	0:24
			Example	0:37
			Subtraction Principle	1:44
			Example	1:48
		Strategy		2:33
			Isolate the Variable	2:41
			Example	2:55
		Example 1: Solve Equation		3:39
		Example 2: Solve Equation		5:38
		Example 3: Word Problem		7:38
		Example 4: Word Problem		11:14
	Multiplication and Division Techniques			15:41
		Intro		0:00
			Isolating the Variable	0:08
		Techniques		0:34
			Multiplication Principle	0:41
			Example	0:57
			Division Principle	2:32
			Example	2:47
		Strategy		3:12
			Example	3:30
			Opposite Operation	3:53
		Example 1: Solve Equation		5:07
		Example 2: Solve Equation		6:50
		Example 3: Solve Equation		10:05
		Example 4: Word Problem		12:07
	Techniques for Multistep Equations			14:31
		Intro		0:00
		What are Multistep Equations		0:06
			Addition/Subtraction and Multiplication/Division	0:31
		Strategy		0:43
			Identify Last Operation	0:47
		Example 1: Solve Equation		1:51
		Example 2: Solve Equation		5:27
		Example 3: Find Numbers		7:39
		Example 4: Solve Equation		11:27
	When the Variable is on Both Sides of the Equation			20:17
		Intro		0:00
		Solving More Complicated Equations		0:28
			Distributive Property	0:41
			Review of Distributive Property	0:55
			Factoring	1:28
			Subtracting	1:50
			Applying with Addition/Subtraction	2:08
		Possible Outcomes		2:45
			Exactly One Solution	2:52
			No Solution	3:08
			True for All Real Numbers	4:45
			Identities	5:01
		Example 1: Solve Equation		6:03
		Example 2: Solve Equation		9:08
		Example 3: Solve Equation		14:06
		Example 4: Solve Equation		17:28
	Ratios and Proportion			16:05
		Intro		0:00
		Definitions		0:07
			Ratio	0:10
			Different Representations	0:14
			Proportion	0:33
			Example	0:40
		Cross Product		1:08
			Cross Multiplication	1:32
			Example	2:13
		Rates		3:33
			Rates in Real Life	3:46
		Example 1: Form a Proportion		4:43
		Example 2: Cross Multiply		7:15
		Example 3: How Long to Drive		9:00
		Example 4: Cross Products		12:13
	Applications of Percents			13:46
		Intro		0:00
		Definitions		0:15
			Percent of Increase	0:27
			Percent of Decrease	0:34
			Examples	0:42
			Sales Tax	1:48
			Discount	2:44
		Example 1: Temperature Change		3:12
		Example 2: Sales Tax		5:44
		Example 3: Clothing Discount		7:04
		Example 4: Sales and Discount		9:15
	More Than One Variable			20:38
		Intro		0:00
		More Than One Variable		0:21
			Real Life Examples	0:30
		Strategy		1:08
			Possible Techniques	1:17
		Typical Application		1:43
			Solving for a Different Variable	1:59
		Example 1: Solve for Y		5:06
		Example 2: Solve for Q		7:38
		Example 3: Solve for H		12:56
		Example 4: Solve for X		16:04
III. Functions
	Relations			16:58
		Intro		0:00
		Definition		0:04
			Relation	0:06
			Table	0:18
			Set of Ordered Pairs	1:01
			Graph	1:38
		Domain and Range		2:40
			Example: Relation	2:51
			Example: Broader Cases	3:48
		Inverse of a Relation		4:42
			Example	4:59
		Example 1: Relation as Table/Graph		6:15
		Example 2: Domain and Range		8:41
		Example 3: Table, Graph, Domain, Range		10:36
		Example 4: Inverse of a Relation		13:36
	Functions			19:27
		Intro		0:00
		Definition		0:14
			Review of Relations	0:27
			Violation of Function	1:43
			Example: Function	2:00
		Vertical Line Test		3:18
			Example	3:41
		Function Notation		6:15
			Using f(x)	6:26
			Example: Value Assigned	7:12
		Example 1: Relation a Function		8:10
		Example 2: Relation a Function		9:39
		Example 3: Using f(x) Notation		12:20
		Example 4: g(x) Notation		15:01
	Linear Functions			20:15
		Intro		0:00
		Definition		0:07
			Standard Form	0:18
			Example	0:52
		Graph and Intercepts		2:39
			Example: Graph	2:48
			X-Intercept	2:56
			Y-Intercept	3:35
		Graphing Linear Equations		4:29
			Example	4:47
		Linear Functions		7:51
			Example	8:15
		Example 1: Linear		10:16
		Example 2: Linear Equation		12:58
		Example 3: Intercepts		14:23
		Example 4: Equation from Intercepts		16:47
IV. Linear Functions and Their Graphs
	Slope and Rate of Change			19:46
		Intro		0:00
		Rate of Change		0:06
			Other Words	0:14
			Example	0:24
		Slope		2:12
			Two Points	2:39
			Steepness of a Line	2:57
		Possible Slopes		4:29
			Positive Slope	5:02
			Negative Slope	5:29
			Zero Slope (Horizontal Line)	6:23
			Undefined Slope (Vertical Line)	7:08
		Example 1: Rate of Change of Table		8:19
		Example 2: Slope Through Points		10:52
		Example 3: Increasing/Decreasing		13:06
		Example 4: Slope Through Points		16:02
	Direct Variation			13:54
		Intro		0:00
		Definitions		0:10
			Constant of Variation k	0:21
			Example: Gas and Miles Driven	0:59
		Graph		1:50
			k is Slope	2:04
			Examples	2:27
		Applications		2:47
			Write, Graph, Solve	2:58
		Example 1: Constant of Variation		3:11
		Example 2: Graph Direct Variation		4:59
		Example 3: Direct Variation		6:50
		Example 4: Distance Car Travels		9:18
	Slope Intercept Form of an Equation			12:06
		Intro		0:00
		Slope Intercept Form		0:12
			m (Slope) and b (Y Intercept)	0:31
			Example	1:12
		Example 1: Slope Intercept Form Equation		2:39
		Example 2: Graph the Equation		5:11
		Example 3: Slope Intercept Form Equation		6:51
		Example 4: Slope Intercept Form Equation		8:50
	Point Slope Form of an Equation			9:07
		Intro		0:00
		Point Slope Form		0:07
			Manipulating to Other Forms	0:35
			m (Slope), x1 y1 (Point)	0:47
		Example 1: Point Slope Form Equation		1:03
		Example 2: Point Slope Form Equation		2:50
		Example 3: Point Slope Form Equation		4:18
		Example 4: Point Slope Form Equation		6:50
	Parallel Lines and Perpendicular Lines			18:02
		Intro		0:00
		Parallel Lines		0:08
			Example	0:15
			Vertical Lines	0:40
		Perpendicular Lines		1:19
			Negative Reciprocal	1:31
			Example	2:05
		Example 1: Slope Intercept Form		3:25
		Example 2: Parallel or Perpendicular		6:15
		Example 3: Slope Intercept Form		9:27
		Example 4: Slope Intercept Form		12:35
V. Systems of Equations
	Graphing Systems of Equations			22:45
		Intro		0:00
		Systems of Equations		0:10
			Definition	0:15
			Example	0:31
			Solution	0:47
		Solving by Graphing		1:23
			Points of Intersection	1:36
			Example	1:56
		Number of Solutions		3:09
			Independent	3:20
			Dependent	3:50
			Inconsistent	4:46
		Example 1: Solve by Graphing		5:45
		Example 2: Solve by Graphing		9:50
		Example 3: Solve by Graphing		14:17
		Example 4: Solve by Graphing		18:03
	Solving by Substituting			22:41
		Intro		0:00
		Substitution		0:09
			Example	0:45
		Number of Solutions		2:47
			Infinite Solutions	3:11
			No Solutions	4:28
		Example 1: Solve by Substitution		5:44
		Example 2: Solve by Substitution		10:01
		Example 3: Solve by Substitution		15:17
		Example 4: Solve by Substitution		19:41
	Solving by Addition and Subtraction			16:13
		Intro		0:00
		Fundamental Principle		0:10
			Example	0:23
		Example 1: Solve the System		1:52
		Example 2: Solve the System		5:53
		Example 3: Solve the System		10:15
		Example 4: Solve the System		14:08
VI. Inequalities
	Addition & Subtraction Techniques			11:34
		Intro		0:00
		Fundamental Principle		0:09
			Example	0:36
		Solutions of Inequalities		1:51
			Inequality	1:59
			Set Builder Notation	2:02
			Graph on a Number Line	2:08
			Examples	2:18
		Example 1: Solve the Inequality		4:59
		Example 2: Solve the Inequality		7:00
		Example 3: Solve the Inequality		8:10
		Example 4: Solve the Inequality		9:47
	Multiplication & Division Techniques			10:49
		Intro		0:00
		Fundamental Principle		0:10
			Only Positive Numbers	0:23
			Example	0:51
		Fundamental Principle, Cont.		2:01
			Negative Numbers	2:12
			Reverse Inequality Sign	2:28
			Example	2:48
		Example 1: Solve the Inequality		4:26
		Example 2: Solve the Inequality		5:45
		Example 3: Solve the Inequality		6:50
		Example 4: Solve the Inequality		8:28
	Techniques for Multistep Inequalities			16:56
		Intro		0:00
		Similarity to Multistep Equations		0:16
			Negative Numbers	0:32
			Example	0:49
		Inequalities Containing Grouping Symbols		1:24
			Example	1:35
		Special Cases		2:45
			Example: All Real Numbers	3:04
			Example: Empty Set	4:10
		Example 1: Solve the Inequality		6:05
		Example 2: Solve the Inequality		7:39
		Example 3: Solve the Inequality		9:57
		Example 4: Solve the Inequality		13:56
	Compound Inequalities			21:32
		Intro		0:00
		What is a Compound Inequality		0:07
			Joined by 'And' or 'Or'	0:16
		Inequalities Combined by 'And'		0:36
			Intersection/Overlap	0:53
			Example	1:08
		Inequalities Combined by 'Or'		4:23
			Union	4:41
			Example	5:27
		Example 1: Solve the Inequality		6:39
		Example 2: Solve the Inequality		11:30
		Example 3: Solve the Inequality		13:43
		Example 4: Solve the Inequality		18:19
	Equations with Absolute Value			24:16
		Intro		0:00
		Absolute Value		0:06
			Number Line	0:22
			Example	0:41
			Absolute Value is N	1:52
		Absolute Value Function		3:17
			Example	3:40
			g(x) and f(x)	4:31
		Solving Absolute Value Equations		6:23
			Absolute Value in Words	6:39
			Split Into Two Parts	7:58
			Solve Both Equations	8:22
		Example 1: Solve the Absolute Value		10:34
		Example 2: Solve the Absolute Value		13:09
		Example 3: Solve the Absolute Value		14:52
		Example 4: Solve the Absolute Value		20:23
	Inequalities with Absolute Values			17:37
		Intro		0:00
		Inequalities of the Form \|x\|< n		0:07
			Values that Satisfy Both Inequalities	0:46
			Example	1:27
		Inequalities of the Form \|x\|> n		3:58
			Values that Satisfy Either Inequalities	4:19
			Example	4:47
		Example 1: Solve the Inequality		6:38
		Example 2: Solve the Inequality		9:54
		Example 3: Solve the Inequality		12:05
		Example 4: Solve the Inequality		14:50
	Graphing Inequalities with Two Variables			24:33
		Intro		0:00
		Graph		0:08
			Half Plane and Boundary	0:51
		Technique for Graphing		1:57
			Graph Equation	2:01
			Solid Line or Dashed Line	2:07
			Example	2:32
			Choosing a Test Point	5:10
			Example	5:26
		Example 1: Solve the Inequality		7:49
		Example 2: Solve the Inequality		11:37
		Example 3: Solve the Inequality		15:44
		Example 4: Solve the Inequality		19:10
	Graphing Systems of Inequalities			24:04
		Intro		0:00
		System of Inequalities		0:05
			Example	0:22
		Solving a System of Inequalities		0:38
			Solution Set	0:46
			Graph Each Inequality	0:57
			Area of Overlap	1:45
		Example 1: Solve the System of Inequalities		2:44
		Example 2: Solve the System of Inequalities		6:33
		Example 3: Solve the System of Inequalities		11:40
		Example 4: Solve the System of Inequalities		17:36
VII. Polynomials
	Multiplying Monomials			22:19
		Intro		0:00
		What is a Monomial		0:09
			Examples	0:17
			Power	0:55
			Base and Exponent	1:52
		Properties of Exponents		2:16
			Add Exponents	2:25
			Multiply Exponents	4:00
			Product Exponent	4:39
		Simplified Form		7:26
			Examples	7:47
		Example 1: Simplify the Monomial		8:26
		Example 2: Simplify the Monomial		10:32
		Example 3: Simplify the Monomial		12:48
		Example 4: Simplify the Monomial		17:33
	Dividing Monomials			24:02
		Intro		0:00
		Properties of Exponents		0:05
		Dividing with Same Base		0:15
			Example	0:53
		Quotient Raised to Power		2:22
			Example	2:53
		Raising to 0 Power		4:00
			Example	4:21
		Negative Exponents		5:45
			Example	6:05
		Example 1: Simplify the Monomial		7:33
		Example 2: Simplify the Monomial		14:56
		Example 3: Simplify the Monomial		13:30
		Example 4: Simplify the Monomial		17:35
	Polynomials			8:56
		Intro		0:00
		What is a Polynomial		0:07
			Monomial	0:40
			Binomial	1:15
			Trinomial	1:25
		Degree of a Polynomial		1:56
			Example: Degree of Monomial	2:13
			Example: Degree of Polynomial	2:47
		Ordering Polynomials		3:32
			Example	3:47
		Example 1: Trinomial or Binomial		4:44
		Example 2: Find the Degree		5:27
		Example 3: Increasing Powers		6:11
		Example 4: Decreasing Powers		7:27
	Adding and Subtracting Polynomials			15:51
		Intro		0:00
		Adding Polynomials		0:07
			Like Terms	0:18
			Example	1:02
		Subtracting Polynomials		2:44
			Example	2:58
		Example 1: Add Polynomials		5:11
		Example 2: Subtract Polynomials		7:30
		Example 3: Add and Subtract		9:35
		Example 4: Add and Subtract		12:09
	Multiplying Polynomials by Monomials			18:17
		Intro		0:00
		Distributive Property		0:07
			Example	0:54
		Solving Equations		1:36
			Isolate Variable and Solve	1:46
		Example 1: Multiply		1:59
		Example 2: Simplify		3:33
		Example 3: Simplify		7:20
		Example 4: Solve		13:37
	Multiplying Polynomials			18:02
		Intro		0:00
		Distributive Property		0:08
			Example	0:54
		FOIL Method		2:44
			First, Outer, Inner, Last	3:20
		Example 1: Multiply		5:32
		Example 2: Multiply		7:27
		Example 3: Multiply		9:41
		Example 4: Multiply		13:56
	Special Products			17:00
		Intro		0:00
		Square of a Sum		0:06
			Example	1:09
		Square of a Difference		2:46
			Example	3:22
		Difference of Two Squares		4:50
			Example	5:31
		Example 1: Multiply		6:24
		Example 2: Multiply		8:34
		Example 3: Multiply		11:03
		Example 4: Multiply		12:54
VIII. Factoring
	Special Product			17:51
		Intro		0:00
		Prime and Composite Numbers		0:09
			Prime Number	0:12
			Composite Number	0:42
		Factored Forms		1:39
			Prime Factored Form	1:40
			Factored Form	2:21
		Greatest Common Factor		3:55
			Example: GCF for Number	4:19
			Example: GCF for Monomial	6:00
		Example 1: Prime Factored Form		7:51
		Example 2: Factored Form		9:34
		Example 3: GCF		11:12
		Example 4: GCF		13:28
	Factoring Using Greatest Common Factor			25:21
		Intro		0:00
		Distributive Property		0:05
			Example: Binomial	0:49
			Example: Trinomial	2:18
		Factoring by Grouping		4:17
			Example: Four Terms	4:40
		Zero Product Property		8:21
			Example	9:01
		Example 1: Factor the Polynomial		10:38
		Example 2: Factor the Polynomial		13:43
		Example 3: Factor the Polynomial		19:59
		Example 4: Solve the Polynomial		22:58
	Factoring Trinomials with Leading Coefficient of 1			27:11
		Intro		0:00
		Factoring Trinomials		0:07
			Leading Coefficient	0:11
			Example	1:20
		Rules for Signs		2:42
			P and Q Both Positive	2:55
			P and Q Both Negative	3:39
			P and Q Opposite Signs	4:30
		Solving Equations		5:18
			Example	6:44
		Example 1: Factor the Polynomial		7:41
		Example 2: Factor the Polynomial		12:33
		Example 3: Factor the Polynomial		16:39
		Example 4: Solve the Polynomial		21:35
	Factoring General Trinomials			46:09
		Intro		0:00
		Factoring Trinomials		0:15
			Example	2:42
		Grouping		7:20
			Example	7:35
		Rules for Signs		10:51
			Same as Leading Coefficient is 1	11:05
		Greatest Common Factor		12:29
			Use Whenever Possible	12:41
			Example	12:59
		Prime Polynomials		13:58
			Example	14:33
		Solving Equations		16:55
			Example	17:25
		Example 1: Factor the Polynomial		18:46
		Example 2: Factor the Polynomial		25:23
		Example 3: Factor the Polynomial		32:37
		Example 4: Solve the Polynomial		36:18
	Factoring the Difference of Two Squares			24:03
		Intro		0:00
		Difference of Two Squares		0:08
			Example	0:36
		Factoring Using Several Techniques		2:23
			Factoring the GCF	2:30
			Example	3:22
		Solving Equations		5:24
			Example	5:50
		Example 1: Factor the Polynomial		7:34
		Example 2: Factor the Polynomial		9:11
		Example 3: Factor the Polynomial		12:00
		Example 4: Solve the Polynomial		18:31
	Factoring Perfect Squares			18:10
		Intro		0:00
		Perfect Squares		0:07
			Example: Perfect Square Trinomials	1:12
		Solving Equations		2:57
			Square Root Property	3:09
			Example	3:28
		Example 1: Factor the Polynomial		5:09
		Example 2: Factor the Polynomial		6:13
		Example 3: Solve the Polynomial		8:43
		Example 4: Solve the Polynomial		13:35
IX. Quadratic Functions
	Graphing Quadratic Functions			35:45
		Intro		0:00
		Parabolas		0:14
			Standard Form of Quadratic Function	0:28
			Examples	1:05
			Absolute Value of 'a'	2:19
		Parabolas That Open Upward		3:14
			Minimum	3:48
			Example	3:57
		Parabolas That Open Downward		6:57
			Example	7:17
			Maximum	9:23
		Vertex		9:53
			Example	10:40
		Axis of Symmetry		14:16
			Example	15:03
		Example 1: Graph the Quadratic		19:54
		Example 2: Graph the Quadratic		24:12
		Example 3: Vertex Maximum or Minimum		28:32
		Example 4: Axis of Symmetry		31:13
	Solving Equations by Graphing			40:42
		Intro		0:00
		Solving a Quadratic Equation		0:08
			Example	0:56
		Two Distinct Solutions/Roots		8:10
			Roots	8:23
			Example: Graphs	8:40
		One Double Root		9:19
			Example: One X-Intercept	9:54
		No Real Roots		14:03
			Example	14:53
		Estimating Solutions		18:41
			Example: Not Integers	19:18
		Example 1: Solve by Graphing		20:18
		Example 2: Solve by Graphing		26:36
		Example 3: Solve by Graphing		30:18
		Example 4: Estimate by Graphing		34:59
	Solving Equations by Completing the Square			28:13
		Intro		0:00
		Perfect Square Trinomials		0:15
			Example	0:36
		Completing the Square		4:55
			Example	6:20
		Completing the Square to Solve Equations		9:19
			Example	9:40
		When the Leading Coefficient is Not 1		13:17
			Example	14:01
		Example 1: Solve the Equation		15:05
		Example 2: Complete the Square		20:16
		Example 3: Solve by Completing the Square		22:31
		Example 4: Solve by Completing the Square		25:02
	Solving Equations Using the Quadratic Formula			17:17
		Intro		0:00
		Quadratic Formula		0:17
			Standard Form	0:24
			Example	1:00
		Discriminant		3:14
			Two Solutions and Both Real	3:40
			One Real Solution	4:07
			No Real Solutions	4:28
		Example 1: Solve the Equation		6:25
		Example 2: Solve the Equation		8:42
		Example 3: Solve the Equation		12:02
		Example 4: Number of Real Roots		15:23
X. Radical Expressions and Equations
	Simplifying Radical Expressions			41:30
		Intro		0:00
		Radical Expression		0:12
			Example: Radicand Simplest Form	0:29
			Example: Not Simplest Form	1:16
			Principal Square Root (Positive)	2:43
		Product Property		3:40
			Examples	4:05
		Square Roots of Variables with Even Powers		7:01
			Eliminate Radical Sign	7:42
			Divide Exponent by 2	7:57
			Absolute Value of Result	8:29
			Examples	8:52
		Quotient Rule		14:12
			Example	14:31
		Rationalizing Denominators		16:08
			Example	16:43
		Conjugates		18:33
			Example	19:53
		Simplest Radical Form		20:58
			Three Criteria	21:10
		Example 1: Simplify Expression		21:57
		Example 2: Simplify Expression		25:12
		Example 3: Simplify Expression		31:37
		Example 4: Simplify Expression		35:29
	Operations with Radical Expressions			21:52
		Intro		0:00
		Adding and Subtracting Radical Expressions		0:13
			Like Radicals	0:28
			Distributive Property	1:10
		Multiplying Radical Expressions		4:24
			Example: Use FOIL	4:44
		Example 1: Simplify Expression		7:07
		Example 2: Simplify Expression		8:51
		Example 3: Simplify Expression		12:14
		Example 4: Simplify Expression		16:06
	Solving Radical Equations			27:00
		Intro		0:00
		Radical Equations		0:15
			Examples	0:30
		Solving a Radical Equation		1:13
			Isolate Radical	1:18
			Square Both Sides	1:38
			Example	1:44
		Extraneous Solutions		2:57
			Example: Check Solutions	3:30
		Example 1: Solve Equation		6:29
		Example 2: Solve Equation		9:52
		Example 3: Solve Equation		14:29
		Example 4: Solve Equation		20:53
	Pythagorean Theorem			17:24
		Intro		0:00
		Right Triangles		0:06
			Vertex	0:32
			Hypotenuse	0:56
			Legs	1:11
		Pythagorean Theorem		1:21
			Graphical Representation	1:37
			Example	2:39
		Pythagorean Triples		3:40
			Example	3:56
		Converse of the Pythagorean Theorem		4:36
			Example	6:23
		Example 1: Length of Hypotenuse		7:24
		Example 2: Length of Legs		9:02
		Example 3: Area of Triangle		12:00
		Example 4: Length of Side		14:59
	Distance Formula			26:50
		Intro		0:00
		Distance Formula		0:09
			Similarity to Pythagorean Theorem	0:21
		Missing Coordinates		5:50
			Example	6:22
		Example 1: Distance Between Points		11:43
		Example 2: Distance Between Points		14:05
		Example 3: Distance Between Points		18:18
		Example 4: Missing Coordinate		21:57
XI. Rational Expressions and Equations
	Inverse Variation			24:13
		Intro		0:00
			Direct Variation	0:12
		Inverse Variation		0:24
			Constant of Variation k	0:50
			Y Varies Inversely as X	0:59
		Graphing Inverse Variation		3:09
			Real World Applications	3:24
			Example	3:59
		Product Rule		10:19
			Alternate Form	11:10
			Finding Missing 4th Point	11:24
		Example 1: Graph Inverse Variation		11:36
		Example 2: Graph Inverse Variation		14:47
		Example 3: Find Missing Point		19:39
		Example 4: Find Missing Point		21:53
	Rational Expressions			34:22
		Intro		0:00
		Rational Expressions		0:10
			Examples	0:28
		Excluded Values		1:03
			Dividing by 0	1:29
			Example	2:49
		Simplifying Rational Expressions		7:12
			Eliminating the GCF	7:17
			Example: Regular Fraction	7:30
			Example: Rational Expression	8:12
		Simplifying and Excluded Values		10:15
			Original Rational Expression	10:24
			Example	10:47
		Example 1: Find Excluded Values		13:47
		Example 2: Simplify and Find Excluded Values		16:10
		Example 3: Simplify and Find Excluded Values		22:04
		Example 4: Simplify and Find Excluded Values		26:29
	Multiplying Rational Expressions			22:58
		Intro		0:00
		Procedure		0:08
			Examples	0:29
		Cancel Before Multiplication		1:53
			Example	2:04
		Rational Expressions Containing Polynomials		3:18
			Example	3:46
		Example 1: Multiply Rational Expressions		6:04
		Example 2: Multiply Rational Expressions		9:11
		Example 3: Multiply Rational Expressions		11:19
		Example 4: Multiply Rational Expressions		17:36
	Dividing Rational Expressions			21:49
		Intro		0:00
		Procedure		0:10
			Reciprocal of Expression	0:22
			Example: Regular Fractions	0:44
			Example: Rational Expressions	1:46
		Cancel Before Multiplying		3:23
			Why Cancel	3:45
			Example	4:15
		Rational Expressions Containing Polynomials		6:46
			Example	7:06
		Example 1: Divide Rational Expressions		9:15
		Example 2: Divide Rational Expressions		13:11
		Example 3: Divide Rational Expressions		15:39
	Dividing Polynomials			35:57
		Intro		0:00
		Dividing a Polynomial by a Monomial		0:11
			Example: Regular Fractions	0:36
			Example: Polynomials	1:24
		Dividing a Polynomial by a Binomial		2:56
			Example: Dividend and Divisor	3:30
		Long Division		5:28
			Example: Regular Numbers	5:49
			Example: Polynomials	7:17
		Missing Terms		12:20
			Definition	12:40
			Example	12:55
		Example 1: Divide the Polynomials		18:42
		Example 2: Divide the Polynomials		20:54
		Example 3: Divide the Polynomials		23:28
		Example 4: Divide the Polynomials		28:52
	Adding and Subtracting Rational Expressions with Like Denominators			17:38
		Intro		0:00
		Adding with Like Denominators		0:09
			Example: Regular Numbers	0:19
			Example: Rational Expressions	1:05
		Subtracting with Like Denominators		2:35
			Example: Regular Fractions	2:52
			Example: Rational Expressions	3:05
		Denominators That Are Additive Inverses		4:08
			What Are Additive Inverses	4:35
			Example	5:53
		Example 1: Add Rational Expressions		7:54
		Example 2: Subtract Rational Expressions		8:43
		Example 3: Add Rational Expressions		10:39
		Example 4: Subtract Rational Expressions		11:48
	Adding and Subtracting Rational Expressions with Unlike Denominators			37:16
		Intro		0:00
		Least Common Multiple of Polynomials		0:21
			Example: Regular Fractions	0:42
			Example: Rational Expressions	5:18
		Equivalent Rational Expressions Using LCM		7:23
			Example	8:09
		Adding and Subtracting		14:24
			Summary of Techniques	14:32
		Example 1: Find the LCM		15:09
		Example 2: Add Rational Expressions		17:53
		Example 3: Subtract Rational Expressions		22:19
		Example 4: Add Rational Expressions		30:44
	Complex Fractions			25:38
		Intro		0:00
		Mixed Expressions		0:10
			Analogy to Mixed Fractions	0:23
			Polynomial and Rational Expression	0:59
			Example: Combining	1:55
			Converting to Rational Expression	2:29
		Complex Fraction		5:16
			Examples	5:30
		Simplifying Complex Fractions		6:08
			Example	6:27
		Example 1: Write as Rational Expression		9:43
		Example 2: Simplify Complex Fractions		12:44
		Example 3: Simplify Complex Fractions		15:03
		Example 4: Simplify Complex Fractions		19:55
	Rational Equations			38:09
		Intro		0:00
		Definition		0:11
			Example: Cross Multiplication	0:39
			Example: Rational Expressions	1:13
		Solving Rational Equations		3:12
			Multiply by LCM of Denominators	3:33
			Example	4:02
		Work Problems		7:19
			Example: Complete a Project	8:17
		Extraneous Solutions		12:41
			Check All Solutions	13:18
			Example	13:54
		Example 1: Solve Rational Equation		17:28
		Example 2: Solve Rational Equation		19:45
		Example 3: Work Problem		27:15
		Example 4: Solve Rational Equation		31:10

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Solving Equations by Graphing

Solving Equations by Graphing

Mathematics: Algebra 1

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