PSAT Math Multiple-Choice Question 515: Answer and Explanation

Question: 515

Which of the following functions represents the parabola graphed in the xy-plane above?

• A. g(x) = –(x – 4)²
• B. g(x) = –x² – 4
• C. g(x) = (x – 4)²
• D. g(x) = x² – 4

Correct Answer: B

Explanation:

B

The question asks for an equation that represents a graph. Pick a point that is on the graph and plug it into the answer choices to see which ones are true. The graph contains the point (0, –4), so plug x = 0 and y = –4 into the answers. Choice (A) becomes –4 = –(0 – 4)² or 4 =(–4)². This becomes 4 = 16, which is false, so eliminate (A). Choice (B) becomes –4 = –0² – 4 or –4 = 0 – 4. This becomes –4 = –4, which is true, so keep (B), but check the other answers just in case. Choice (C) becomes –4 = (0 – 4)² or 4 =(–4)². This becomes 4 = 16, which is false, so eliminate (C). Choice (D) becomes –4 = 0² – 4 or –4 = 0 – 4. This becomes –4 = –4, which is true. To differentiate between (B) and (D), either plug in another point or remember that parabolas that open downward correspond to a quadratic equation with a negative sign in front of the x² term. In (D), the sign of the x² term is positive. Eliminate (D). The correct answer is (B).