# 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:

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.