SAT Math Multiple Choice Question 713: Answer and Explanation

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Question: 713

8. If the function f is defined by the equation f(x) = k(x + 6)(x - 1), where k > 5, then which of the following is equivalent to f(7)?

  • A. f(-78)
  • B. f(-12)
  • C. f(-2)
  • D. f(78)

Correct Answer: B

Explanation:

B

Advanced Mathematics (analyzing quadratics) HARD

One way to tackle this question is simply to simplify the expression for f(7), and then see which choice gives the same expression.

f(7) = k(7 + 6)(7 - 1) = k(13)(6) = 78k

Evaluate (A):

f(-78) = k(-78 + 6)(-78 - 1) = k(-72)(-79) = 5,688k

Evaluate (B):

f(-12) = k(-12 + 6)(-12 - 1) = k(-6)(-13) = 78k

Evaluate (C):

f(-2) = k(-2 + 6)(-2 - 1) = k(4)(-3) = -12k

Evaluate (D):

f(78) = k(78 + 6)(78 - 1) = k(84)(77) = 6,468k

This shows that f(-12) is equal to f(7). Alternately, you might just make a quick sketch of the parabola and take advantage of the symmetry:

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