ASVAB Mathematics Knowledge Practice: Quadratic Equations

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:

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

   

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:

   

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:

   

   Set each factor equal to 0; then solve:

   

   The solutions are x = 0 and x = 3.