Algebra II : Quadratic Equations and Inequalities

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #10 : Quadratic Inequalities

Which value for  would satisfy the inequality ?

Possible Answers:

Not enough information to solve

Correct answer:

Explanation:

First, we can factor the quadratic to give us a better understanding of its graph. Factoring gives us: . Now we know that the quadratic has zeros at  and . Furthermore this information reveals that the quadratic is positive. Using this information, we can sketch a graph like this: 

Sketch inequality

We can see that the parabola is below the x-axis (in other words, less than ) between these two zeros  and .

The only x-value satisfying the inequality  is .

The value of  would work if the inequality were inclusive, but since it is strictly less than instead of less than or equal to , that value will not work.

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