SAT Math Multiple Choice Question 931: Answer and Explanation

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Question: 931

15. What is the range of the quadratic function whose equation is q(x) = –(x + 4)2 + 3?

  • A.
  • B.
  • C.
  • D.

Correct Answer: B

Explanation:

B

Difficulty: Medium

Category: Passport to Advanced Math / Quadratics

Strategic Advice: The range of a function is the set of outputs that the function takes on, or in other words, the set of y-values through which the graph of the function passes.

Getting to the Answer: Use your knowledge of parabolas to draw a quick sketch of the function. You are only interested in the y-values of the graph, so plot the vertex and sketch the direction in which the parabola opens. Don't worry about the x-intercepts or any other specific points on the graph. The equation is written in vertex form, y = a(x - h)2 + k, so you know the vertex is (-4, 3). Because a is negative (-1), the parabola opens downward, so your sketch should look like the following:

The y-values of the graph start below the x-axis and go up to the y-value of the vertex (3), so the range of the function is given by y ≤ 3, which is (B).

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