1. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Quadratic Inequalities ♦ Solve quadratic inequalities graphically ♦ Solve quadratic inequalities symbolically 3.3

2. Slide 3- 2 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Quadratic Inequalities

3. Slide 3- 3 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Graphical Solutions

4. Slide 3- 4 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Solve the inequality. Write the solution set for each in interval notation. a) 3x 2 + x  4 = 0b) 3x 2 + x  4 < 0 c) 3x 2 + x  4 > 0 Solution

5. Slide 3- 5 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Solution continued

6. Slide 3- 6 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example The quadratic inequality can be used to compute stopping distances in feet for a car traveling x miles per hour on dry, level pavement. Solve the inequality shown below to determine safe speeds on a curve where a driver can see the road ahead for at most 150 feet. Solution

7. Slide 3- 7 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

8. Slide 3- 8 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Solve x 2 > 7x – 10 symbolically. Write the solutions in interval notation. Solution

9. Slide 3- 9 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Solution continued Step 4: Choose test values. IntervalTest Value xx 2 – 7x + 10Positive or Negative? (– , 2) 0 (2, 5)3 (5,  ) 6