A25-7 Quadratic Inequalities

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A25-7 Quadratic Inequalities

  1. 1. Quadratic Inequalities 5.7 Algebra 2
  2. 2. Graphing Inequalities Draw the parabola and shade the area indicated by the inequality.
  3. 3. Graphing Inequalities y > x2 - 2x -3 Use a graphing calculator to draw the parabola. (http://www.coolmath.com/graphit/)
  4. 4. Graphing Inequalities y > x2 - 2x -3 Or use your notes from 5.1 :) Find the vertex and the axis of symmetry
  5. 5. Systems of Quadratic Inequalities Graph both parabolas first using a graphing calculator.
  6. 6. Systems of Quadratic Inequalities Graph both parabolas first. Then shade the areas indicated.
  7. 7. Systems of Quadratic Inequalities Graph both parabolas first. Then shade the areas indicated. The solution to the system is the part that is shaded by all inequalities. (If there are no overlapping spots, there is no solution.)
  8. 8. Solving Inequalities Solve the equation to find the “critical x-values.”
  9. 9. x2 + 2x ≤ 8 ⇒ x2 + 2x - 8 ≤ 0 Solve for 0.
  10. 10. x2 + 2x ≤ 8 ⇒ x2 + 2x - 8 ≤ 0 (x - 2)(x + 4) ≤ 0 Factor.
  11. 11. x2 + 2x ≤ 8 ⇒ x2 + 2x - 8 ≤ 0 (x - 2)(x + 4) ≤ 0 x - 2 = 0 and x + 4 = 0 Solve for x. x = 2 and x = -4.
  12. 12. Solving Inequalities Solve the equation to find the “critical x-values.” Plot the critical numbers on a number line. 0-4 2
  13. 13. Solving Inequalities Solve the equation to find the “critical x-values.” Plot the critical numbers on a number line. Notice that this breaks the number line up into 3 sections.
  14. 14. Solving Inequalities Solve the equation to find the “critical x-values.” Plot the critical numbers on a number line. Test a number inside each region. 0-4 2
  15. 15. [-4, 2] is the solution. Use square brackets if “less than or equal to.” Use parentheses if just “less than” or “greater than.”

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