PSAT Math Multiple-Choice Question 61: Answer and Explanation

Question: 61

Which of the following equations has a vertex of (-5, 2)?

• A. y = (x + 5)² - 2
• B. y = (x -5)² - 2
• C. y = 2(x + 5)² + 2
• D. y = 2(x - 5)² + 2

Correct Answer: C

Explanation:

C

The question asks for an equation with a vertex of (-5, 2). There are variables in the answer choices, so plug in. Use the given point to make x = -5 and y = 2. Now plug x = -5 and y = 2 into the answer choices to see which one is true. Choice (A) becomes 2 = (-5 + 5)² - 2 = (0)² - 2 = -2. Since 2 = -2 is not true, eliminate (A). Choice (B) becomes 2 = (-5 - 5)² - 2 = (-10)² - 2 = 100 - 2 = 98, which is not true. Eliminate (B). Choice (C) becomes 2 = (2)(-5 + 5)² + 2 = 2(0)² + 2 = 0 + 2 = 2. Keep (C), but check (D) just in case. Choice (D) becomes 2 = 2(-5 - 5)² + 2 = 2(-10)² + 2 = 2(100) + 2 = 200 + 2 = 202. Eliminate (D). The correct answer is (C).