ASVAB AFQT
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When you run into a problem on the Mathematics Knowledge subtest on the ASVAB that deals with quadratic equations, you can use different ways to solve it: by factoring, completing the square, or using the quadratic formula.

The quadratic formula for equations in the form of ax2 + bx + c = 0 looks like this:

ASVAB_1401

Practice questions

  1. Express as a quadratic equation: 2x2 – 8x – 4 = 3x – x2

    A. x2 – 11x – 4 = 0 B. 3x2 – 11x – 4 = 0 C. 3x2 – 5x – 4 = 0 D. 3x2 – 11x – 3 = 0

  2. Solve for x: x2 – 3x = 0

    ASVAB_1402

Answers and explanations

  1. The correct answer is Choice (B).

    A quadratic equation has an x2 term. When the equation is in standard form, both sides equal 0. Put all the terms on the same side, set the other side equal to 0, and combine like terms:

    ASVAB_1403

  2. The correct answer is Choice (A).

    A quadratic equation's standard form is ax2 + bx + c = 0. Although this equation shows only two terms, x2 and –3x, it's still quadratic because there's an x2 term (you can assume c = 0).

    Solve this quadratic equation by factoring:

    ASVAB_1404

    Set each factor equal to 0; then solve:

    ASVAB_1405

    The solutions are x = 0 and x = 3.

About This Article

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About the book author:

Angie Papple Johnston joined the U.S. Army in 2006 as a Chemical, Biological, Radiological, and Nuclear specialist, ready to tackle chemical weapons in a Level- A HAZMAT suit. She's currently the CBRN noncommissioned officer-in-charge of an aviation battalion in Washington, D.C.

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