slide 6 - 1 copyright © 2009 pearson education, inc. 6.9 continued solving quadratic equations by...
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Slide Copyright © 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.TRANSCRIPT
Slide 6 - 1Copyright © 2009 Pearson Education, Inc.
6.9 Continued
Solving Quadratic Equations by Using Factoring and by Using the Quadratic Formula
Slide 6 - 2Copyright © 2009 Pearson Education, Inc.
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
Slide 6 - 6Copyright © 2009 Pearson Education, Inc.
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