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Quadratic Inequalities Lesson 3.4 Definition Recall the quadratic equation ax2 + bx + c = 0 Replace = sign with <, >, ≤, or ≥ makes it a quadratic inequality Solving: Find where the equality occurs These values are the boundary numbers 2 Graphical Solutions Graph of the quadratic y = ax2 + 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 3 Try It Out Given 2 x 5 x 2 0 Place in Y= screen, graph 2 3.14 x 0.64 Determine boundary values (zeros of equation) Which values of x satisfy the inequality? 4 Another Version Consider 2x2 > 16 Create a graph of both sides of the inequality Determine values of x which satisfy the equation, then the inequality x 2 2 or x2 2 5 Steps for Symbolic Solution 1. Write as an equation ax2 + 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 6 Example Try x2 – 9 < 0 Solve x2 – 9 = 0 x = +3 or x = -3 x y • • -5 16 -2 -5 This is the interval 7 40 3 x 3 7 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 x2 – 9 < 0 8 Assignment Lesson 3.4 Page 218 Exercises 1 – 53 EOO 9