SAT Math Multiple Choice Question 321: Answer and Explanation

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Question: 321

6. Which of the following equations could represent a parabola that has a minimum value of –5 and whose axis of symmetry is the line x = 1?

  • A. y = (x – 5)2 + 1
  • B. y = (x + 5)2 + 1
  • C. y = (x – 1)2 – 5
  • D. y = (x + 1)2 – 5

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Passport to Advanced Math / Quadratics

Strategic Advice: Imagine the graph of a parabola. The minimum value is the y-coordinate of its vertex, and the axis of symmetry also passes through the vertex. Use these properties to identify the vertex, and then use it to write the equation of the parabola in vertex form, y = a(x - h)2 + k, where (h, k) is the vertex.

Getting to the Answer: If the minimum of the parabola is -5, then the vertex of the parabola looks like (x, -5). The axis of symmetry, x = 1, tells you the x-coordinate-it's 1. That means (h, k) is (1, -5), and the equation of the parabola looks like y = a(x - 1)2 - 5. The value of a in each of the answer choices is 1, so (C) is correct.

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