PSAT Math Multiple-Choice Question 59: Answer and Explanation

Question: 59

Which of the following equations is shown in the graph above?

• A. y = -(x - 3)(x + 1)
• B. y = -(x + 3)(x - 1)
• C. y = -(x + 3)(x + 4)
• D. y = -(x - 1)(x + 4)

Correct Answer: B

Explanation:

B

The question asks for an equation that matches the graph. The answer choices are quadratic equations that have already been factored, so use the roots from the graph to eliminate wrong answers. The roots, or solutions, of a graph are where it crosses the x-axis: look at the graph to see that the correct solutions will be -3 and 1. Eliminate (C) and (D) which have a 4 in one of the factors instead of 1 and 3. To decide between (A) and (B), plug in a point from the graph. The vertex appears to be at (-1, 4). Plug x = -1 and y = 4 into (A) to get 4 = -(-1 - 3)(-1 + 1). This becomes 4 = -(-4)(0) or 4 = 0. This is not true, so eliminate (A), but check (B) just in case. Choice (B) becomes 4 = -(-1 + 3)(-1 - 1) or 4 = -(2)(-2). This simplifies to 4 = 4. The correct answer is (B).