PSAT Math Multiple-Choice Question 459: Answer and Explanation

Question: 459

Which of the following represents the function shown in the graph?

• A.
• B.
• C.
• D.

Correct Answer: B

Explanation:

B

Difficulty: Medium

Getting to the Answer: The parabola opens downward, so the a term should be negative. Unfortunately, all the choices have a negative a term, so you're not able to eliminate any of them. All of the choices appear to be in vertex form, so take a look at the graph: the vertex appears to be at (3, 2); only (A) and (B) match this. To decide between them, plug in some values from points on the graph, such as the two x-intercepts, (2, 0) and (4, 0). Check if f (2) = 0 for (A): -((2) - 3)² + 2 = -(-1)² + 2 = -(1) + 2 = 1. Eliminate (A) because f (2) ≠ 0. Only (B) is left and is correct. For this equation, both x = 2 and x = 4 produce a result of f(x) = 0.