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4.9 – Graph and Solve Quadratic Inequalities

4.9 – Graph and Solve Quadratic Inequalities. A quadratic inequality in two variables can be written in one of the following forms: y < ax 2 + bx + c y < ax 2 + bx + c y > ax 2 + bx + c y > ax 2 + bx + c

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4.9 – Graph and Solve Quadratic Inequalities

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  1. 4.9 – Graph and Solve Quadratic Inequalities A quadratic inequality in two variables can be written in one of the following forms: y < ax2 + bx + c y < ax2 + bx + c y > ax2 + bx + c y > ax2 + bx + c The graph of any such inequality consists of all solutions (x, y) of the inequality.

  2. 4.9 – Graph and Solve Quadratic Inequalities

  3. 4.9 – Graph and Solve Quadratic Inequalities Example 1a: Graph a quadratic inequality Graph y > x2 + 3x – 4

  4. 4.9 – Graph and Solve Quadratic Inequalities Example 1b: Graph a quadratic inequality Graph y < -x2 – 4x

  5. 4.9 – Graph and Solve Quadratic Inequalities Example 2: A manila rope used for rappelling down a cliff can safely support a weight W (in pounds) provided W < 1480d2 where d is the rope’s diameter (in inches). Graph the inequality.

  6. 4.9 – Graph and Solve Quadratic Inequalities Example 3: Graph the system of quadratic inequalities. y < -x2 + 4 y > x2 – 2x – 3

  7. 4.9 – Graph and Solve Quadratic Inequalities Example 3: Graph the system of quadratic inequalities. y < -x2 + 4 y > x2 – 2x – 3

  8. 4.9 – Graph and Solve Quadratic Inequalities A quadratic inequality in one variablecan be written in one of the following forms: ax2 + bx + c < 0 ax2 + bx + c < 0 ax2 + bx + c > 0 ax2 + bx + c >0 You can solve quadratic inequalities using tables, graphs, or algebraic methods.

  9. 4.9 – Graph and Solve Quadratic Inequalities Example 4: Solve x2 + x < 6 using a table.

  10. 4.9 – Graph and Solve Quadratic Inequalities Example 4b: Solve x2 + 2x > 8 using a table.

  11. 4.9 – Graph and Solve Quadratic Inequalities Example 5: Solve 2x2 + x – 4 > 0 by graphing.

  12. 4.9 – Graph and Solve Quadratic Inequalities Example 5b: Solve ½x2 + 3x – 2 < 0 by graphing.

  13. 4.9 – Graph and Solve Quadratic Inequalities Example 6: Solve x2 – 2x > 15 by algebraically.

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