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Set 16: Quadratic Equations (Intermediate)

Explanation

Answer: A

Find the vertex of y=x2+2y = x^2 + 2.

A.

(0,2)(0, 2)

✓ Correct
B.

(2,0)(2, 0)

C.

(0,0)(0, 0)

D.

(2,0)(-2, 0)

Detailed Explanation

Choice A is correct. Choice A is the correct answer. This equation is in the form y=ax2+cy = ax^2 + c, where b=0b=0. 1. Calculate x-coordinate: x=b/2a=0/2(1)=0x = -b/2 a = -0/2(1) = 0. 2. Calculate y-coordinate: y=02+2=2y = 0^2 + 2 = 2. Alternatively, recognize this as a vertical shift of the parent function y=x2y=x^2 up by 2 units. The vertex moves from (0,0)(0,0) to (0,2)(0,2). Choice B is incorrect because it swaps x and y. Choice C is incorrect because it ignores the constant term. Choice D is incorrect because it confuses horizontal and vertical shifts.

Key Steps:

The correct answer is (0,2)(0, 2)

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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