# 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).