PSAT Math Multiple-Choice Question 476: Answer and Explanation

Question: 476

Which of the following coordinates is the vertex of the parabola y = x² - 14x + 3?

• A. (7, -46)
• B. (-7, -46)
• C. (14, -193)
• D. (-14, -193)

Correct Answer: A

Explanation:

A

Difficulty: Hard

Category: Completing the Square

Strategic Advice: Vertex form is usually a good option when questions ask for coordinates of the vertex. One of the best methods to convert quadratic equations into vertex form is completing the square.

Getting to the Answer: The x² term has a coefficient of 1, so no manipulation of the equation is necessary before completing the square. Move the constant term to the right side of the equation before dividing the x term's coefficient by 2 and squaring:

Now the equation y = (x - 7)² - 46 is in vertex form, y = a(x - h)² + k, where the vertex is (h, k). To find the x-coordinate of the vertex, or h, be aware of the negative sign before h in vertex form. In this case, -h = -7, so h = 7. Only (A) has an x-coordinate of 7, so it must be correct.

For the record, the y-coordinate, or k, of the vertex is -46. The vertex therefore is (h, k) = (7, -46), so (A) is indeed correct.