SAT Math Multiple Choice Question 931: Answer and Explanation
15. What is the range of the quadratic function whose equation is q(x) = –(x + 4)2 + 3?
Correct Answer: B
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).