4 9 Graph and Solve Quadratic Inequalities A

4. 9 – Graph and Solve Quadratic Inequalities Example 1 a: Graph a quadratic

4. 9 – Graph and Solve Quadratic Inequalities Example 1 b: Graph a quadratic

4. 9 – Graph and Solve Quadratic Inequalities Example 2: A manila rope used

4. 9 – Graph and Solve Quadratic Inequalities Example 3: Graph the system of

4. 9 – Graph and Solve Quadratic Inequalities A quadratic inequality in one variable

4. 9 – Graph and Solve Quadratic Inequalities Example 4: Solve x 2 +

4. 9 – Graph and Solve Quadratic Inequalities Example 4 b: Solve x 2

4. 9 – Graph and Solve Quadratic Inequalities Example 5: Solve 2 x 2

4. 9 – Graph and Solve Quadratic Inequalities Example 5 b: Solve ½x 2

4. 9 – Graph and Solve Quadratic Inequalities Example 6: Solve x 2 –

Slides: 13

Download presentation

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

4. 9 – Graph and Solve Quadratic Inequalities Example 1 a: Graph a quadratic inequality Graph y > x 2 + 3 x – 4

4. 9 – Graph and Solve Quadratic Inequalities Example 1 b: Graph a quadratic inequality Graph y < -x 2 – 4 x

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 < 1480 d 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 2 + 4 y > x 2 – 2 x – 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 4 b: Solve x 2 + 2 x > 8 using a table.

4. 9 – Graph and Solve Quadratic Inequalities Example 5: Solve 2 x 2 + x – 4 > 0 by graphing.

4. 9 – Graph and Solve Quadratic Inequalities Example 5 b: Solve ½x 2 + 3 x – 2 < 0 by graphing.

4. 9 – Graph and Solve Quadratic Inequalities Example 6: Solve x 2 – 2 x > 15 by algebraically.