This document discusses quadratic inequalities and how to solve them. It defines quadratic inequalities as expressions of the form ax^2 + bx + c < 0, = 0, or > 0, where a, b, and c are real numbers and a does not equal 0. It provides examples of solving quadratic inequalities by determining the sign of the expression over different intervals of the domain. It also applies the concepts to an example word problem about determining the possible dimensions of a parking space that is less than 40 square meters.

1. Section 7
Chapter 9

2. 1
Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Objectives
2
3
QUADRATIC INEQUALITIES
Illustrate quadratic inequalities.
Solve quadratic inequalities.
Solve problems involving quadratic inequalities.
9.7

3. Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Quadratic Inequality
A quadratic inequality can be written in the form
ax2 + bx + c < 0 or ax2 + bx + c > 0,
ax2 + bx + c ≤ 0 or ax2 + bx + c ≥ 0,
where a, b, and c are real numbers, with a ≠ 0.
Slide 9.7- 3
Solve quadratic inequalities.

4. Copyright © 2012, 2008, 2004 Pearson Education, Inc.
EXAMPLES
Slide 9.7- 4

5. Copyright © 2012, 2008, 2004 Pearson Education, Inc.
SOLVE
Slide 9.7- 5
Region
Test
point
value
(x+1)(x-3) < 0 Result
A
B
C

6. Copyright © 2012, 2008, 2004 Pearson Education, Inc.
SOLVE
Slide 9.7- 6
Region
Test
point
value
Result
A
B
C

7. Copyright © 2012, 2008, 2004 Pearson Education, Inc.
SOLVE
Slide 9.7- 7
Region
Test
point
value
Result
A
B
C

8. Copyright © 2012, 2008, 2004 Pearson Education, Inc.
Application
Slide 9.7- 8
Mrs. Reyna is planning to fence her vacant lot for a parking space.
The desired length of the lot is 6 meters longer than its width.
What will be the possible dimensions of the rectangular parking
space if it should be less than 40sqm?