# 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) = 78*k*

Evaluate (A):

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

Evaluate (B):

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

Evaluate (C):

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

Evaluate (D):

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

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: