# SAT Math Multiple Choice Question 658: Answer and Explanation

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**Question: 658**

**13.** *y* = *a*(*x* + 3)(*x* - 1)

In the quadratic function above, *a* is a nonzero constant. The graph of the equation in the *xy*-plane is a parabola with vertex (*m*, *n*). Which of the following is equal to *n*?

- A. 0
- B. -
*a* - C. -2
*a* - D. -4
*a*

**Correct Answer:** D

**Explanation:**

**D**

**Advanced Mathematics (analyzing quadratics) HARD**

Original equation:

*y* = *a(x* + 3)(*x* - 1)

This equation represents a quadratic in *x*. Since it is in factored form, it shows us that the function has *x*-intercepts (also known as zeroes or roots) when *x* + 3 = 0 or *x* - 1 = 0, so its *x*-intercepts are at *x* = -3 and *x* = 1. Recall (from Chapter 9, Lesson 6) that a parabola representing a quadratic function has an axis of symmetry at *x* = *k*, where *k* is midway between the *x*-intercepts. Therefore, *k* = (-3 + 1)/2 = -1. This axis of symmetry, *x* = -1, must pass through the vertex. We can get the *y*-coordinate of this vertex by just plugging *x* = -1 back into the function:

*y* = *a*(-1 + 3)(-1- 1)

Simplify:

*y* = *a*(2)(-2) = -4*a*