SAT Math Multiple Choice Question 608: Answer and Explanation

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Question: 608

8. Which of the following equations represents a parabola in the xy-plane with a vertex that lies on the x-axis?

  • A. y = (x - 3)2 + 2
  • B. y = 2(x - 3)2
  • C. y = 2x2 - 3
  • D. y = 3x2 + 2

Correct Answer: B

Explanation:

B Advanced Mathematics (parabolas) MEDIUM

The general equation of a parabola in the xy-plane is y = a(x - h)2 + k, in which (h, k) is the vertex. Now let's express each choice in precisely this form.

(A) y = (x - 3)2 + 2 y = 1(x - 3)2 + 2 a = 1, h = 3, k = 2

(B) y = 2(x - 3)2 y = 2(x - 3)2 + 0a = 2, h = 3, k = 0

(C) y = 2x2 - 3 y = 2(x - 0)2 - 3a = 2, h = 0, k = -3

(D) y = 3x2 + 2 y = 3(x - 0)2 + 2a = 3, h = 0, k = 2

If this vertex is on the x-axis, then k = 0. The only equation in which k = 0 is (B).

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