On the SAT Math exam, you will probably encounter a quadratic function or two, so it’s important to remember that they come in two forms: y = ax2 + bx + c or f (x) = ax2 + bx + c. (Don’t panic; they mean the same thing.)

The following practice questions may look scary, but they simply involve a little distribution, simplifying, and plugging in of values.

Practice questions

  1. Given this equation, what is the value of a + b + c? x(2x + 3) – 2(x – 3) = ax2 + bx + c
  2. If a, b, and c are integers, 6x2 + cx + 6 = (ax + 2)(bx + 3) for all values of x, and 1 < a < b, what is the value of c?

Answers and explanations

  1. The correct answer is 9. Distribute and simplify the expressions on the left to match the quadratic on the right:
    From this, you know that a = 2, b = 1, and c = 6, which add up to 9.
  2. The correct answer is 12. Multiply the binomials to match the quadratic, and then simplify by subtracting 6 from both sides:
    Because 6x2 = abx2, ab = 6. And because a and b are integers and 1 < a < b, you know that a = 2 and b = 3. Now, using cx = (3a + 2b)x, you can plug in 2 for a and 3 for b and then solve for c:

About This Article

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Ron Woldoff is the founder of National Test Prep, where he helps students prepare for the SAT, GMAT, and GRE. He is the author of several books, including GRE For Dummies and 1,001 GRE Practice Questions For Dummies.

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