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. -2a
  • D. -4a

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) = -4a

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