Exit Pass: Solving Quadratic Inequalities

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What is a quadratic inequality?

Back

A quadratic inequality is an inequality that involves a quadratic expression, typically in the form ax² + bx + c < 0, ax² + bx + c > 0, ax² + bx + c ≤ 0, or ax² + bx + c ≥ 0.

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How do you solve a quadratic inequality?

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1. Rewrite the inequality in standard form. 2. Find the roots of the corresponding quadratic equation. 3. Use a number line to test intervals defined by the roots. 4. Determine where the inequality holds true.

Front

What does the solution set of a quadratic inequality represent?

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The solution set represents the values of x for which the quadratic expression is either less than or greater than zero, depending on the inequality.

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What is the significance of the roots in a quadratic inequality?

Back

The roots of the quadratic equation help to divide the number line into intervals, which are tested to determine where the inequality is satisfied.

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What does it mean if a quadratic inequality has no solution?

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It means that there are no values of x that satisfy the inequality, often occurring when the quadratic expression is always positive or always negative.

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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.

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How do you graph the solution of a quadratic inequality?

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1. Plot the roots on a number line. 2. Use open circles for strict inequalities and closed circles for non-strict inequalities. 3. Shade the regions that satisfy the inequality.

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What is the vertex of a quadratic function?

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The vertex is the highest or lowest point of the parabola represented by the quadratic function, found at the point (h, k) where the function is in vertex form y = a(x-h)² + k.

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What is the axis of symmetry in a quadratic function?

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The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a) for a quadratic in standard form.

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What does it mean if a quadratic inequality is always true?

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It means that the quadratic expression is either always greater than or equal to zero or always less than or equal to zero for all real numbers.