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Warm Up

Write as an inequality. Warm Up. Remember having to graph. Remember having to graph. Graphing Quadratic Inequalities. Lesson 3.9. Steps for Graphing (quickly). Graph the vertex Use the slope (1, 3, 5…) to get the other points (if a = 1) For <> use DASHED for ≤≥ use SOLID line

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Warm Up

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  1. Write as an inequality. Warm Up

  2. Remember having to graph

  3. Remember having to graph

  4. Graphing Quadratic Inequalities Lesson 3.9

  5. Steps for Graphing (quickly) • Graph the vertex • Use the slope (1, 3, 5…) to get the other points (if a = 1) • For <> use DASHED for ≤≥ use SOLID line 4. Shade the appropriate region (greater shade above the vertex, less shade below the vertex)

  6. Shading

  7. Graph: y ≤ x2 + 6x – 4 * Vertex: (-3,-13) Slope 1, 3, 5 * Solid Line * Less than means shade BELOW

  8. Graph: y > -x2 + 4x – 3 * Vertex: (2, 1) Slope -1, -3, -5 * Dashed Line * Greater than means shade ABOVE

  9. Graph: y ≥ x2 – 8x + 12 * Vertex: (4, -4) Slope 1, 3, 5 * Solid Line * Greater than means shade ABOVE

  10. Graph: y > -x2 + 4x + 5 * Vertex: (2, 9) Slope -1, -3, -5 * Dashed Line * Greater than means shade ABOVE

  11. Solving a Quadratic Inequality

  12. Steps for solving • Write the original inequality as an equation • Set equal to 0, factor, and solve. • Plot the points on a number line and test points in each interval back into the original inequality. • Write the answer (the TRUE part) as an inequality

  13. Solve: x2 – 5x≤ – 4 x2 – 5x = -4 x2 – 5x + 4 = 0 (x – 4) (x – 1) = 0 x = 1, 4 False True   False Answer: 1 ≤ x ≤ 4

  14. Solve: -x2 + 7x< 12 -x2 + 7x = 12 -x2 + 7x – 12 = 0 x2 – 7x + 12 = 0 (x – 4) (x – 3) = 0 x = 3, 4 False True True   Answer: x < 3 or x > 4

  15. What if it can’t factor?Graph it!

  16. Solve: -(x – 1)2 – 3 < 0 -(x – 1)2 – 3 < y y > -(x – 1)2 – 3 Answer: all real numbers

  17. Solve: x2 + 4 ≤ 0 x2 + 4 ≤ y y ≥ x2 + 4 Answer: no solution

  18. Workbookp. 110 #13 – 18

  19. HW Textbookp. 98 #1 – 18p. 99 #28, 31 – 33(solve algebraically)

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