Quadratic Inequalities Lesson 3 3 Definition l l

Quadratic Inequalities Lesson 3. 3

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

Graphical Solutions l Graph of the quadratic y = ax 2 + bx + c is a parabola l l l 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 3

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

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

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

Example Try x 2 – 9 < 0 l Solve x 2 – 9 = 0 l x = +3 or x = -3 x y • • -5 16 -2 -5 7 40 This is the interval 7

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

Assignment l l l Lesson 3. 3 Page 195 Exercises 1 – 39 odd 9