SAT Math Multiple Choice Question 538: Answer and Explanation

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Question: 538

13. Given the equation y = -3(x – 5)2 + 8, which of the following statements is not true?

  • A. The y-intercept is (0, 8).
  • B. The axis of symmetry is x = 5.
  • C. The vertex is (5, 8).
  • D. The parabola opens downward.

Correct Answer: A

Explanation:

A

Difficulty: Hard

Category: Passport to Advanced Math / Quadratics

Strategic Advice: To answer this question, you need to recall nearly everything you've learned about quadratic graphs. The equation is given in vertex form (y = a(x – h)2 + k), which reveals the vertex (h, k), the direction in which the parabola opens (upward when a > 0 and downward when a < 0), the axis of symmetry (x = h), and the minimum/maximum value of the function (k).

Getting to the Answer: Start by comparing each answer choice to the equation, y = –3(x – 5)2 + 8. The only choice that you cannot immediately compare is (A), because vertex form does not readily reveal the y-intercept, so start with B. Don't forget, you are looking for the statement that is not true. Choice B: The axis of symmetry is given by x = h, and h is 5, so this statement is true and therefore not correct. Choice C: The vertex is given by (h, k), so the vertex is indeed (5, 8) and this choice is not correct. Choice D: The value of a is –3, which indicates that the parabola opens downward, so this choice is also incorrect. That means (A) must be the correct answer. To confirm, you could substitute 0 for x in the equation to find the y-intercept.

The y-intercept is (0, –67), not (0, 8), so the statement is not true and therefore the correct answer.

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