5
advanced-math

Identify the vertex of y=2(x+1)2−4y = 2(x + 1)^2 - 4.

A

(−1,−4)(-1, -4)

B

(1,−4)(1, -4)

C

(−1,4)(-1, 4)

D

(1,4)(1, 4)

Correct Answer: A

Choice A is the correct answer. The equation is in vertex form y=a(x−h)2+ky = a(x - h)^2 + k.

  1. Compare x+1x + 1 to x−hx - h. This means h=−1h = -1.
  2. Compare −4-4 to +k+k. This means k=−4k = -4.
  3. Vertex is (h,k)=(−1,−4)(h, k) = (-1, -4).

Choice B is incorrect because of sign error on x. Choice C is incorrect because of sign error on y. Choice D is incorrect because of sign errors on both.

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Set 7: Quadratic Equations and Functions 7