5.2.1 Solving Quadratic Inequalities Key Objectives • Solve quadratic inequalities by using tables and graphs. • Solve quadratic inequalities by using algebra. Key Terms • A quadratic inequality in two variables is an inequality that can be written in one of the following forms, where a , b , and c are real numbers and a ≠ 0.
• y < ax 2 + bx + c • y ≤ ax 2 + bx + c • y > ax 2 + bx + c • y ≥ ax 2 + bx + c
Example 1 Graphing Quadratic Inequalities in Two Variables Use the following steps to graph a quadratic inequality. 1. Graph the parabola that defines the boundary.
2. Use a solid parabola for y ≤ or y ≥ and a dashed parabola for y < or y > . 3. Shade above the parabola for y ≥ or y > and below the parabola for y ≤ or y < .
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