SAT Math Multiple Choice Question 682: Answer and Explanation

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Question: 682

7. The value of y varies with x according to the equation y = a(x - 2)(x + 1), where a < 0. As the value of x increases from 0 to 5, which of the following best describes the behavior of y?

  • A. It increases and then decreases.
  • B. It decreases and then increases.
  • C. It increases only.
  • D. It decreases only.

Correct Answer: A

Explanation:

A

Advanced Mathematics (quadratics) MEDIUM-HARD

The graph of y = a(x - 2)(x + 1) is a quadratic with zeros (x-intercepts) at x = 2 and x = -1. The axis of symmetry of this parabola is halfway between the zeros, at x = (2 + -1)/2 = 1/2. Since a < 0, the parabola is "open down," and so we have a general picture like this:

Images

If you trace the curve from x = 0 to x = 5, that is, from the y-intercept and then to the right, you can see that the graph goes up a bit (until x = 1/2), and then goes down again.

Alternately, you can pick a negative value for a (like - 2) and graph the equation on your calculator.

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