2. Graphing and Solving Quadratic Inequalities CHAPTER 5 LESSON 8

3. Vocabulary Quadratic Inequality- A quadratic equation in the form y≥ax 2 +bx+c, y≤ax 2 +bx+c, y ax 2 +bx+c

4. Graphing a Quadratic Inequality Step 1- Graph the quadratic function, if the inequality is, it should be a dotted line, if it is ≤ or ≥, then it should be a solid line. Step 2- Test a point inside the parabola, plug in the values of x and y into the equation, check to see if the point is a solution Step 3- If the point is a solution, shade inside the parabola, if the point is not a solution, shade outside of the parabola.

5. Graph a Quadratic Inequality by Table xy -5-2 -41 -32 -21 -2 y > -x 2 – 6x – 7 Vertex is at -3

6. Example y ≤ x 2 + 2x + 4 Vertex? xy

7. Example y > -2x 2 + 3x + 5 Vertex? xy

8. Solving Quadratic Inequalities when ax 2 +bx+c < 0 Graph the equation ax 2 +bx+c = 0 If a > 0, then the x values between the two x-intercepts are solutions to the inequality If a < 0, then the x values that are not between the two x-intercepts are solutions to the inequality If the inequality is <, do not include the intercepts as solutions If the inequality is ≤, then include the intercepts as solutions

9. What that means in English…..

10. Example

12. Solving Quadratic Inequalities when ax 2 +bx+c > 0 Graph the equation ax 2 +bx+c = 0 If a < 0, then the x values between the two x-intercepts are solutions to the inequality If a > 0, then the x values that are not between the two x- intercepts are solutions to the inequality If the inequality is >, do not include the intercepts as solutions If the inequality is ≥, then include the intercepts as solutions

13. What it means in English..

14. Example

16. Solving Quadratic Inequalities Solve x 2 + x > 6 algebraically x 2 + x = 6 x 2 + x – 6 = 0

17. Test a Value in Each Interval to See if the Inequality is True X < -3-3 < x < 2X > 2 Test x = -4Test x = 0Test x = 4 x 2 + x > 6 (-4) 2 + (-4) > 6(0) 2 + (0) > 6(4) 2 + (4) > 6 12 > 60 > 620 > 6

18. Example Solve x 2 + 5x < -6

19. Example

20. Solve x 2 + 11x + 30 ≥ 0

21. Example

22. Homework Worksheet 5-8

23. Chapter Review Page 307 1-30