1. Quadratic Inequalities Lesson 3.4

2. 2 Definition Recall the quadratic equation ax 2 + bx + c = 0 Replace = sign with, ≤, or ≥ makes it a quadratic inequality Solving: Find where the equality occurs These values are the boundary numbers

3. 3 Graphical Solutions Graph of the quadratic y = ax 2 + bx + c is a parabola Extends upward or downward Solution to y > 0 includes all x-values where graph is above the axis Solution to y < 0 includes x-values where graph is below the axis

4. 4 Try It Out Given Place in Y= screen, graph Determine boundary values (zeros of equation) Which values of x satisfy the inequality?

5. 5 Another Version Consider 2x 2 > 16 Create a graph of both sides of the inequality Determine values of x which satisfy the equation, then the inequality or

6. 6 Steps for Symbolic Solution 1. Write as an equation ax 2 + bx + c = 0 Solve resulting equation for boundary numbers 2. Use boundary numbers to separate number line into disjoint intervals 3. Make a table of test values One value from each interval 4. Use this to specify which intervals satisfy the original inequality

7. 7 Example Try x 2 – 9 < 0 Solve x 2 – 9 = 0 x = +3 or x = -3 x-5-27 y16-540 This is the interval

8. 8 Using the Calculator Table Place function in the Y= screen Go to Table, ♦Y Adjust start, increment as needed, F2 View intervals where results are negative, zero, or positive x 2 – 9 < 0

9. 9 Assignment Lesson 3.4 Page 218 Exercises 1 – 53 EOO