Slide 6 - 1Copyright © 2009 Pearson Education, Inc.

6.9 Continued

Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula

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Solving Quadratic Equations by Factoring

Standard Form of a Quadratic Equation

ax2 + bx + c = 0, a 0

Zero-Factor Property

If a • b = 0, then a = 0 or b = 0.

Slide 6 - 3Copyright © 2009 Pearson Education, Inc.

To Solve a Quadratic Equation by Factoring

Use the addition or subtraction property to make one side of the equation equal to 0.

Factor the side of the equation not equal to 0. Use the zero-factor property to solve the

equation.

Slide 6 - 4Copyright © 2009 Pearson Education, Inc.

Example: Solve by Factoring

Solve 4x2 + 17x 15 = 0.

The solutions are 5 and ¾.

0534 xx

034 x 05x34 x 5x

43

xor

Slide 6 - 5Copyright © 2009 Pearson Education, Inc.

Solve by factoring

02422 xx

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Practice Problem: Solve by factoring

07236 2 xx

Slide 6 - 7Copyright © 2009 Pearson Education, Inc.

Quadratic Formula

For a quadratic equation in standard form, ax2 + bx + c = 0, a 0, the quadratic formula is

2 42

b b acxa

Slide 6 - 8Copyright © 2009 Pearson Education, Inc.

Example: Using the Quadratic Formula

Solve the equation 3x2 + 2x 7 = 0.

a = 3, b = 2 and c = 7

2 42

b b acxa

32

73422 2

68442

6882

62222

3221

Slide 6 - 9Copyright © 2009 Pearson Education, Inc.

Practice Problem: solve using the quadratic equation

0153 2 xx

Slide 6 - 10Copyright © 2009 Pearson Education, Inc.

Homework: P 360 # 35 – 77 eoo