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Holt Algebra 2 5-7 Solving Quadratic Inequalities DÉJÀ VU: Graphing Linear Inequalities Graph the inequality. The boundary line is which has a 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.

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Holt Algebra 2 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.

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

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

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Holt Algebra 2 5-7 Solving Quadratic Inequalities Graph y x 2 – 7x + 10. Example 1: Graphing Quadratic Inequalities in Two Variables Step 1 Graph the boundary of the related parabola y = x 2 – 7x + 10 with a solid curve. Its y-int is (0,10), its vertex is (3.5, –2.25).

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

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Holt Algebra 2 5-7 Solving Quadratic Inequalities Graph the inequality. Step 1 Graph the boundary of the related parabola y = 2x 2 – 5x – 2 with a solid curve. Its y-int is (0,–2), its vertex is (1.3, –5.1). Example 2 y 2x 2 – 5x – 2

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

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

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

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

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Holt Algebra 2 5-7 Solving Quadratic Inequalities Notes 4. For y x 2 + 9x + 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

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