PSAT Math Multiple-Choice Question 113: Answer and Explanation

Question: 113

If the equation x = (y + 5)(y - 15) is graphed in the xy-plane, what is the y-coordinate of the parabola's vertex?

• A. 5
• B. 10
• C. 25
• D. 100

Correct Answer: A

Explanation:

A

The question asks for the y-coordinate of a parabola's vertex. The question gives the equation of a parabola in factored form, which makes it easy to determine the solutions, or y-intercepts in this case. Because parabolas are symmetrical about a central axis that runs through the vertex, the y-coordinate of the vertex will be halfway between the two y-intercepts. If x = 0, then the equation becomes 0 = (y + 5)(y - 15). Set each binomial equal to 0 to get y + 5 = 0 and y - 15 = 0, so y = - 5 or 15. Eliminate (C) and (D), which aren't between the intercepts at all. To find the midpoint, average the y-intercepts to get . Ine correct answer is (A).