# SAT Math Multiple Choice Question 845: Answer and Explanation

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**Question: 845**

**5.** The data in which of the following scatterplots would be best modeled by a quadraticfunction in which the *x*^{2} term has a negative coefficient?

- A.
- B.
- C.
- D.

**Correct Answer:** D

**Explanation:**

**D**

**Difficulty:** Easy

**Category:** Problem Solving and Data Analysis / Scatterplots

**Strategic Advice:** Data that can be modeled by a quadratic function should take the shape of a parabola (or part of a parabola), which looks like a U. Part of the data should increase from left to right, and part of the data should decrease (at some point, the data turns around).

**Getting to the Answer:** The data in choice A follows a linear pattern, so eliminate it. The data in C is curved, but it is always decreasing (it never turns around), which means it can't be modeled by a quadratic function, so eliminate it as well. To choose between B and (D), recall that a negative coefficient on the *x*^{2} term means the parabola opens downward (because it has been reflected vertically across the *x*-axis). This means (D) is correct.