3

Set 11: Quadratic Equations (Intermediate)

Explanation

Answer: A

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

A.

(−1,−4)(-1, -4)

✓ Correct
B.

(1,−4)(1, -4)

C.

(−1,4)(-1, 4)

D.

(1,4)(1, 4)

Detailed Explanation

Choice A is correct. 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.

Key Steps:

•

The correct answer is (−1,−4)(-1, -4)

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.
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