PSAT Math Multiple-Choice Question 63: Answer and Explanation

Question: 63

The stream of water that shoots out of a public fountain in Central Park takes the form of a parabola. The water shoots from a spout that is 8 feet above the ground and reaches a maximum height of 39.25 feet. If y represents the height of the water and x represents the time (in seconds), which of the following equations could describe the trajectory of the stream of water?

• A. y = -x² + 15
• B. y = -5x² + 25x + 8
• C. y = 2x² + 32x + 8
• D. y = 8x + 39.25

Correct Answer: B

Explanation:

B

The question asks for an equation that models a specific situation. Translate the question in Bite-Sized Pieces and eliminate after each piece. One piece of information says that the correct equation should be a parabola. The standard form of a parabola equation is y = ax² + bx + c. The equation should include an x² term, so eliminate (D), which is a linear equation. The value of a tells whether a parabola open upwards (positive a) or downwards (negative a). Since the water from the fountain shoots up and then down, the parabola should open downwards and have a negative value for a. Eliminate (C), which has a positive value for a. Compare the remaining answers. The important difference between (A) and (B) is the c term. The question states that the fountain's spout is 8 feet above the ground. Since y is the height of the water and x is the time from the spout, y = 8 when x = 0. Plug x = 0 into (A) to see if whether becomes y = 8. Choice (A) becomes y = -0² + 15 = 15. This means y = 8 does not appear in (A), so eliminate (A). The correct answer is (B).