Quadratic Inequality

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What is a quadratic inequality?

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How do you solve a quadratic inequality?

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1. Solve the corresponding quadratic equation to find critical points. 2. Use these points to divide the number line into intervals. 3. Test each interval to determine where the inequality holds true.

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What is the significance of critical points in quadratic inequalities?

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Critical points are the values of x where the quadratic expression equals zero. They help to determine the intervals to test for the solution of the inequality.

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What does the graph of a quadratic inequality represent?

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The graph represents the regions of the coordinate plane where the quadratic expression satisfies the inequality (either above or below the x-axis, depending on the inequality).

Tags

CCSS.HSA.REI.D.12

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The solution set is the union of intervals where the quadratic expression is positive, which can be found by testing intervals around the critical points.

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How do you represent the solution set of a quadratic inequality on a number line?

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The solution set is represented by shading the regions of the number line that satisfy the inequality, using open or closed circles to indicate whether endpoints are included.

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It implies that x is either less than -6 or greater than -5, as these are the intervals where the quadratic expression is positive.

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What is the difference between strict and non-strict inequalities?

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Strict inequalities (<, >) do not include the boundary points, while non-strict inequalities (≤, ≥) include the boundary points in the solution set.

Tags

CCSS.6.EE.B.8