PSAT Math Multiple-Choice Question 449: Answer and Explanation

Question: 449

Which of the following equations has the same solutions as x² + 6x +17 = y?

• A. y = (x - 3)² - 26
• B. y = (x - 3)² + 8
• C. y = (x + 3)² + 8
• D. y = (x + 3)² + 17

Correct Answer: C

Explanation:

C

Difficulty: Medium

Strategic Advice: Equations that are equivalent have the same solutions, so you are looking for the equation that is simply written in a different form. You could expand each of the equations in the answer choices, but unless you get lucky, this strategy will use up quite a bit of time. The answer choices are written in vertex form, so use the method of completing the square to rewrite the equation given in the question stem.

Getting to the Answer: First, subtract the constant, 17, from both sides of the equation. To complete the square on the right-hand side, find and add the result to both sides of the equation:

Next, factor the right-hand side of the equation (which should be a perfect square trinomial), and rewrite it as a square. Finally, solve for y:

This matches (C).