5 7 Solving Quadratic Inequalities DJ VU Graphing

5 -7 Solving Quadratic Inequalities DÉJÀ VU: Graphing Linear Inequalities Graph the inequality The boundary line is y-int of (0, 2) and a slope of Draw the boundary line dashed because it is not part of the solution. Then shade the region above the boundary line to show. Holt Algebra 2 . which has a.

5 -7 Solving Quadratic Inequalities Earlier we solved linear inequalities in two variables by graphing. We can use a similar procedure to graph quadratic inequalities. Holt Algebra 2

5 -7 Solving Quadratic Inequalities Notes 1. For A) f(x)= -x 2 + 7 B) f(x)= x 2 + 8 x - 20 C) f(x)= -2(x-3)2 +7 Identify the vertex, and state the domain and range 2. For y > (x+1)2 – 3 A. State shifts B. Find vertex C. Graph (and shade) 3. For y > -x 2 – 4 x A. Up or downward B. Find vertex C. Graph (and shade) 4. For y ≤ x 2 + 9 x + 14 Holt Algebra 2 A. Up or downward B. Find vertex C. Find y-intercept D. Graph (& shade)

5 -7 Solving Quadratic Inequalities Notes 1. Identify the vertex, state the domain and range for A) f(x)= -x 2 + 7 B) f(x)= x 2 + 8 x – 20 C) f(x)= -2(x-3)2 +7 2. For y = (x+1)2 – 3 A. State shifts B. Find vertex C. Graph y > (x+1)2 – 3 (and shade) Holt Algebra 2

5 -7 Solving Quadratic Inequalities Example 1: Graphing Quadratic Inequalities in Two Variables Graph y ≥ x 2 – 7 x + 10. Step 1 Holt Algebra 2 Graph the boundary of the related parabola y = x 2 – 7 x + 10 with a solid curve. Its y-int is (0, 10), its vertex is (3. 5, – 2. 25).

5 -7 Solving Quadratic Inequalities Example 1 Continued Step 2 Holt Algebra 2 Shade above the parabola because the solution consists of y-values greater than those on the parabola for corresponding x-values.

5 -7 Solving Quadratic Inequalities Example 2 Graph the inequality. y ≥ 2 x 2 – 5 x – 2 Step 1 Holt Algebra 2 Graph the boundary of the related parabola y = 2 x 2 – 5 x – 2 with a solid curve. Its y-int is (0, – 2), its vertex is (1. 3, – 5. 1).

5 -7 Solving Quadratic Inequalities Example 2 Continued Step 2 Holt Algebra 2 Shade above the parabola because the solution consists of y-values greater than those on the parabola for corresponding x-values.

5 -7 Solving Quadratic Inequalities Example 3 Graph each inequality. y < – 3 x 2 – 6 x – 7 Step 1 Holt Algebra 2 Graph the boundary of the related parabola y = – 3 x 2 – 6 x – 7 with a dashed curve. Its y-intercept is (0, – 7).

5 -7 Solving Quadratic Inequalities Example 3 Continued Step 2 Holt Algebra 2 Shade below the parabola because the solution consists of y-values less than those on the parabola for corresponding x-values.

5 -7 Solving Quadratic Inequalities Notes 3. For y > -x 2 – 4 x A. Up or downward B. Find vertex C. Graph (and shade) 4. For y ≤ x 2 + 9 x + 14 A. Up or downward B. Find vertex C. Find y-intercept D. Graph (and shade) Holt Algebra 2

5 -7 Solving Quadratic Inequalities Notes 4. For y ≤ x 2 + 9 x + 14 A. State whether it opens upward or downward B. Find the vertex C. Find the y-intercept D. Graph the boundary line E. Shade Holt Algebra 2