SAT Math Multiple Choice Question 845: Answer and Explanation

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Test Information

Question: 845

5. The data in which of the following scatterplots would be best modeled by a quadraticfunction in which the x2 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 x2 term means the parabola opens downward (because it has been reflected vertically across the x-axis). This means (D) is correct.

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