Solving Quadratic Equations by Factoring

1
Section 5.2

• Solving Quadratic Equations by Factoring

• Factor quadratic expressions and solve quadratic
• equations by factoring.
• Find zeros of quadratic functions.

2
Warm Up

• Solve the equation
• 3x 4 0
• 2x 11 -15
• -3x 5 2x
• 2(x 3) 6

3
Vocabulary

• (x 3)(x 5) ? x2 8x 15
• binomials
• trinomial
• factoring

4
What Do You Notice?

• (x 3)(x 5) ?turn into standard form.

5
Factoring a Trinomial

• x2 bx c (x m)(x n)
• x2 (m n)x mn

6
Example 1 Factoring a Trinomial of the form x2
bx c

• Factor x2 12x 28
• Factors of c

7
Try these problems

• pg. 260-261
• 23-25

8
Example 2 Factoring a Trinomial in the form ax2
bx c

• Factor 3x2 17x 10

9
Try these problems

• pg. 260-261
• 35-37

10
Factoring with Special Patterns
11
Example 3 Factoring with Special Patterns

• Factor the quadratic expression
• 4x2 25
• 9y2 24y 16
• 49r2 14r 1

12
Try these problems

• pg. 260-261
• 47-49

13
Monomials

• an expression that has only one term
• example 3(2x 1)(5x 7)
• the monomial is ______
• As a first step to factoring, you should check
  to see whether the terms have a common monomial
  factor.

14
Example 4 Factoring Monomials First

• Factor the quadratic expression
• 5x2 20
• 6p2 15p 9
• 2u2 8u
• 4x2 4x 4

15
Try these problems

• pg. 260-261
• 56-58

16
Solving Quadratic Equations

• ax2 bx c 0 where a ? 0.
• if the left side can be factored the equation can
  be solved using the ZERO PRODUCT PROPERTY.
• Let A and B be real numbers or algebraic
  expressions. If AB 0 then A 0 or B 0.

17
Example 5 Solving Quadratic Equations

• Solve
• x2 3x 18 0
• 2x2 17x 45 0

18
Try these problems

• pg. 260-261
• 65-67

19
Example 6 Using Quadratic Equations as a Model

• You have made a rectangular stained glass window
• that is 2 feet by 4 feet. You have 7 square feet
  of clear
• glass to create a boarder of uniform width around
  the
• window. What should the width around the boarder
• be?

20
Try these problems

• pg. 260-261
• 74-76

21
Zeros

• y a(x p)(x q)
• x-int
• the numbers p and q are also called __________ of
  the function because the functions value is zero
  when x p and when x q.

22
Try these problems

• pg. 260-261
• 80-82

23
Example 8 Using Zeros of a Quadratic Model

• You maintain a music-oriented Web site that
  allows
• subscribing customers to download audio and music
• clips of their favorite bands. When the
  subscription
• price is 16 per year, you get 30,000
  subscribers. For
• each 1 increase in price, you expect to loose
  1000
• subscribers. How much should you charge to
• maximize your annual revenue? What is your
• maximum revenue?

24
Try these problems

• pg. 260-261
• 91