3 3 Quadratic Inequalities Solve quadratic inequalities graphically

3. 3 Quadratic Inequalities ♦ Solve quadratic inequalities graphically ♦ Solve quadratic inequalities symbolically Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

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

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

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

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

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 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 3 - 6

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

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

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