PSAT Math Multiple-Choice Question 471: Answer and Explanation

Question: 471

Which of the following equations could represent a parabola that has a minimum value of -3 and whose axis of symmetry is the line x = 2?

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

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Graphs of Quadratics

Getting to the Answer: When a quadratic equation is written in vertex form, y = a(x - h)² + k, the minimum value (or the maximum value if a < 0) is given by k, and the axis of symmetry is given by the equation x = h. The question states that the minimum of the parabola is -3, so look for an equation where k = -3. You can eliminate choices (A) and (B) because k = 2 in both equations. The question also states that the axis of symmetry is x = 2, so h must be 2. Be careful: this can be tricky. The equation in choice (D) is not correct because the vertex form of a parabola includes the term (x - h) not (x + h), so (x + 2) should be interpreted as (x - (-2)), with axis of symmetry at x = -2. This means (C) is correct.