Algebra 2 Completing the Square

V. Quadratic Functions and Inequalities: Lecture 5 | 16:42 min

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Completing the Square

You can solve quadratic equations by taking the square root of both sides of the equation. To do this, the quadratic expression must be a perfect square.
Complete the square to make the quadratic expression into a perfect square. Take one half of the coefficient of the linear term, square it, and add it to both sides of the equation.
If the coefficient of the quadratic term is not 1, you must first factor this coefficient out of the quadratic and linear term and then complete the square for the new quadratic expression which now has a coefficient of 1.

Completing the Square

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

Square Root Property

Examples

Completing the Square

Example: Making into Perfect Square

Solve Equations

Example

Equations Where 'a' Not Equal to 1

Example

Complex Solutions

Example

Lecture Example 1

Lecture Example 2

Additional Example 3

Additional Example 4

Intro 0:00
Square Root Property 0:22

Examples

Completing the Square 1:48

Example: Making into Perfect Square

Solve Equations 3:43

Example

Equations Where 'a' Not Equal to 1 6:47

Example

Complex Solutions 10:14

Example

Lecture Example 1 11:30
Lecture Example 2 12:34
Additional Example 3
Additional Example 4

Mathematics: Algebra 2

I. Equations and Inequalities
	Expressions and Formulas	28:56
	Properties of Real Numbers	23:45
	Solving Equations	24:41
	Solving Absolute Value Equations	17:36
	Solving Inequalities	19:27
	Solving Compound and Absolute Value Inequalities	24:08
II. Linear Relations and Functions
	Relations and Functions	38:15
	Linear Equations	12:50
	Slope	20:07
	Writing Linear Functions	27:36
	Special Functions	24:28
	Graphing Inequalities	30:37
III. Systems of Equations and Inequalities
	Solving Systems of Equations by Graphing	21:27
	Solving Systems of Equations Algebraically	31:26
	Solving Systems of Inequalities by Graphing	20:43
	Solving Systems of Equations in 3 Variables	21:27
IV. Matrices
	Basic Matrix Concepts	14:08
	Matrix Operations	16:40
	Matrix Multiplication	22:47
	Determinants	25:47
	Cramer's Rule	25:42
	Identity and Inverse Matrices	27:01
	Solving Systems of Equations with Matrices	28:40
V. Quadratic Functions and Inequalities
	Graphing Quadratic Equations	26:36
	Solving Quadratic Equations by Graphing	19:26
	Solving Quadratic Equations by Factoring	17:46
	Imaginary and Complex Numbers	37:41
	Completing the Square	16:42
	Quadratic Formula and the Discriminant	17:44
	Analyzing the Graphs of Quadratic Functions	23:00
	Graphing and Solving Quadratic Inequalities	34:38
VI. Polynomial Functions
	Properties of Exponents	20:28
	Operations on Polynomials	16:13
	Dividing Polynomials	29:26
	Polynomial Functions	29:34
	Analyzing Graphs of Polynomials	34:36
	Solving Polynomial Equations	19:23
	Remainder and Factor Theorems	27:52
	Roots and Zeros	31:04
	Rational Zero Theorem	29:27
VII. Rational Equations and Inequalities
	Operations on Functions	35:12
	Inverse Functions and Relations	18:12
	Square Root Functions and Inequalities	26:24
	nth Roots	24:06
	Operations with Radical Expressions	34:38
	Rational Exponents	24:36
	Solving Radical Equations and Inequalities	38:46
VIII. Radical Expressions and Equations
	Multiplying and Dividing Rational Expressions	30:11
	Adding and Subtracting Rational Exprsesions	51:53
	Graphing Rational Functions	45:13
	Direct, Joint, and Inverse Variation	21:49
	Solving Rational Equations and Inequalities	53:21
IX. Exponential and Logarithmic Relations
	Exponential Functions	28:22
	Logarithms and Logarithmic Functions	36:31
	Properties of Logarithms	29:50
	Common Logarithms	27:10
	Base 'e' and Natural Logarithms	19:52
	Exponential Growth and Decay	28:10
X. Conic Sections
	Midpoint and Distance Formulas	29:35
	Parabolas	26:11
	Circles	17:33
	Ellipses	38:57
	Hyperbolas	37:59
	Conic Sections	23:10
	Solving Quadratic Systems	28:18
XI. Sequences and Series
	Arithmetic Sequences	27:44
	Arithmetic Series	29:12
	Geometric Sequences	24:52
	Geometric Series	27:02
	Infinite Geometric Series	24:01
	Recursion and Special Sequences	17:11
	Binomial Theorem	38:25
	Proof and Mathematical Induction	19:53

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Algebra 2 Completing the Square

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Completing the Square

Mathematics: Algebra 2

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