PSAT Math Multiple-Choice Question 162: Answer and Explanation

Question: 162

In the xy-plane, the graph of the function f is a parabola. If the graph off intersects the x-axis at (k, 0) and (3, 0), and the vertex of f is at (5, -3), what is the value of k?

• A. 9
• B. 7
• C. 5
• D. 1

Correct Answer: B

Explanation:

B

The question asks for the value of k, which is the x-coordinate of one of the x-intercepts. According to the question, the graph of f is a parabola, which means it has vertical symmetry. In a parabola, the axis of symmetry goes through the vertex. Since the vertex is at (5, -3), the axis of symmetry is x = 5. Since one of the x-intercepts is (3, 0), the other must be equidistant from the axis of symmetry. Since the distance from 3 to 5 is 2, the distance from 5 to k must also be 2. Therefore, k = 5 + 2 = 7. The correct answer is (B).