PSAT Math Multiple-Choice Question 470: Answer and Explanation

Question: 470

Shawna throws a baseball into the air. The equation h = -5(t² - 4t + 4) + 22 represents the height of the ball in meters t seconds after it is thrown. Which of the following equations could represent the height of a second ball that was thrown by Meagan, if Meagan's ball did not go as high as Shawna's ball?

• A. h = -10(t - 4)² + 27
• B. h = -10(t - 2)² + 25
• C. h = -8(2t - 1)² + 23
• D. h = -5(t - 2)² + 21

Correct Answer: D

Explanation:

D

Difficulty: Hard

Category: Graphs of Quadratics

Getting to the Answer: Look for an equation among the choices that has a maximum value that is less than the maximum height of Shawna's toss. To determine the peak height of Shawna's throw, convert the given equation to vertex form, y = a(x - h)² + k, where the maximum value is given by k. Notice that the polynomial within the parentheses factors to(t - 2)². Thus, you can restate the given equation as -5(t - 2)² + 22. So the vertex of the equation for Shawna's throw is (2, 22), which means that the maximum height was 22 meters.

Conveniently, the choices are all stated in vertex form. The only one with the k term less than 22 is (D), which makes that the correct choice. (Notice that this equation differs from the restated version of the given equation only by the k term.)