4. 4 Solving Quadratic Inequalities

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What is a quadratic inequality?

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How do you solve a quadratic inequality?

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To solve a quadratic inequality, first solve the corresponding quadratic equation to find the critical points. Then, test intervals between these points to determine where the inequality holds true.

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What are critical points in the context of quadratic inequalities?

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What does the graph of a quadratic function look like?

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What is the significance of the vertex in a quadratic function?

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The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction the parabola opens. It represents the maximum or minimum value of the function.

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What does it mean for a quadratic expression to be greater than zero?

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What does it mean for a quadratic expression to be less than or equal to zero?

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How do you determine the intervals for a quadratic inequality?

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After finding the critical points, test values from each interval created by these points in the original inequality to see if they satisfy the inequality.

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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.

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