9.2 Solving Quadratics by Completing the Square.notebook March 08, 2016

March 8thQuiz on Friday

Due Next Class:  9.2 HW & Video Notes

Get Ready:

Unit 9: Quadratic Functions

Lesson 9.2 ­ Solving Quadratic Equations that are Unfactorable...or too difficult to factor

1) What does it mean to solve the equation x2 + 5x ­ 14 = 0 ?

2) Solve the following equations.

Hint: How can you check if your solution(s) is correct?

a. 5n2 + 14n + 3 = 6n + 4n2 ­ 4 b. x2 ­ 2x = 12

9.2 Solving Quadratics by Completing the Square.notebook March 08, 2016

Homework Review

9.2 Solving Quadratics by Completing the Square.notebook March 08, 2016

Mathematical Magic

How can we use that to solve (x+4)2 = 25

What number multiplied by itself equals 25?

Conclusion: If we take the square root of a number, then...

Solve: (x ­ 3)2 = 49

9.2 Solving Quadratics by Completing the Square.notebook March 08, 2016

How to Solve Unfactorable Quadratic Equations

Could we get x2 ­ 2x = 12 to look like (x­1)2 = 13 so we can solve it?

Is (x­1)2 = 13 a quadratic equation?

9.2 Solving Quadratics by Completing the Square.notebook March 08, 2016

Steps for Solving Unfactorable Quadratic Equations

Completing the Square

1) Divide everything by a (the coefficient of x2)

2) Move the constant term to the right side of the equation

3) Divide b (the coefficient of x) by 2 and then square it

4) Add that square number to each side of the equation

5) Factor the quadratic trinomial on the left side of the equation ­ Should factor a perfect square trinomial

6) Solve for x

9.2 Solving Quadratics by Completing the Square.notebook March 08, 2016

x2 ­ 2x = 12

Completing the Square

1) Divide everything by a (the coefficient of x2)

2) Move the constant term to the right side of the equation

3) Divide b (the coefficient of x) by 2 and then square it

4) Add that square number to each side of the equation

5) Factor the quadratic trinomial on the left side of the equation ­ Should factor to a perfect square trinomial

6) Solve for x

3) b = 2

2= =

4) x2 ­ 2x + = 12 +

x2 ­ 2x ­ 12 = 0

9.2 Solving Quadratics by Completing the Square.notebook March 08, 2016

What are the advantages to Completing the Square?

Allows us to solve quadratic equations that are not factorable