PSAT Math Multiple-Choice Question 689: Answer and Explanation

Question: 689

What happens to the vertex (h, k) of y = x² + 3 if the 3 is replaced by a 6 and if x is changed to (x - 5)?

• A. h decreases by 5, k increases by 6
• B. h increases by 5, k increases by 3
• C. h increases by 5, k increases by 6
• D. h remains the same, k increases by 31

Correct Answer: B

Explanation:

(B) The vertex form of a parabola is y = (x - h)² + k, where (h, k) are the coordinates of the vertex. Our original equation can be written in this form as y = (x - 0)² + 3. So h = 0 and k = 3.

The second parabola would be written as y = (x - 5)² + 6. So h = 5 and k = 6.

Therefore, h increases by 5 and k increases by 3, which is choice (B).