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.

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Presentation transcript:

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 The graph of any such inequality consists of all solutions (x, y) of the inequality.

4.9 – Graph and Solve Quadratic Inequalities

Example 1a: Graph a quadratic inequality Graph y > x 2 + 3x – 4

4.9 – Graph and Solve Quadratic Inequalities Example 1b: Graph a quadratic inequality Graph y < -x 2 – 4x

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 < 1480d 2 where d is the rope’s diameter (in inches). Graph the inequality.

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

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

4.9 – Graph and Solve Quadratic Inequalities A quadratic inequality in one variable can be written in one of the following forms: ax 2 + bx + c < 0 ax 2 + bx + c > 0 You can solve quadratic inequalities using tables, graphs, or algebraic methods.

4.9 – Graph and Solve Quadratic Inequalities Example 4: Solve x 2 + x < 6 using a table.

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

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

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

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