Algebra 1 Common Core Student Edition, Grade 8-9

Factoring to Solve

Quadratic Equations

Objective To solve quadratic equations by factoring

Co m m o n Co r e St a t e St a n d a r d s

A-REI.B.4b Solve quadratic equations by...

factoring. .. Also A-SSE.B.3a, A-CED.A.1, F-IF.C.8a

MP 1, MP 2, MP 3, M P4, MP 7

Get t i n g Read y! «► x C

Analyze the

situation. W h a t

expressions can

you use fo r th e

len g th and fo r th e

width?

You a re finishing a stained glass hanging t h a t your

friend has started. You have enough supplies to

add 6 f t 2 to th e hanging. You a re planning to add

the same amount to the length and width. What

will be th e dimensions o f th e hanging when you

a re finished? How do you know?

x

I

m

MATHEMATICAL

PRACTICES In the previous lesson, you solved quadratic equations ax2 + bx + c = 0 by finding

square roots. This method works if b = 0.

Lesso n

Vocabulary

• Z ero-P rod u ct
  Property

Essent ial Und er st and ing You can solve some quadratic equations, including

equations where b + 0, by using the Zero-Product Property.

The Multiplication Property of Zero states that for any real number a, a • 0 = 0. This is

equivalent to the following statement: For any real numbers a and b, if a = 0 or b = 0,

then ab = 0. The Zero-Product Property reverses this statement.

Pr o p er t y Zero-Product Propert y

For any real numbers a and b, if ab = 0, then a = 0 or b = 0.

Example If (x + 3 )(jc + 2) = 0, thenx + 3 = 0 o r x + 2 = 0.

Think.

How else can you

write the solutions?

You can w rite th e

so lu tio n s as a set in

roster form: { - j L 2 }.

Pr o b l em 1 Using t he Zero-Product Propert y

What are the solutions of the equation (4f + l )(f — 2) = 0?

(4 f+ l)(t — 2) = 0

4f + 1 = 0 or t — 2 = 0 Use the Zero-Product Property.

4f=—1 or t = 2 Solve f o r t ,

(^1) or t = 2
J
568 Chapter 9 Quadratic Functions and Equations