4

Set 12: Quadratic Equations

Explanation

Answer: A

Which equation corresponds to a parabola that opens upward with a vertex at (0,−4)(0, -4)?

A.

y=x2−4y = x^2 - 4

✓ Correct
B.

y=−x2−4y = -x^2 - 4

C.

y=(x−4)2y = (x - 4)^2

D.

y=x2+4y = x^2 + 4

Detailed Explanation

Choice A is correct. Choice A is the correct answer. 1. Vertex at (0,−4)(0, -4): This implies a vertical shift down 4 units, so k=−4k = -4 and h=0h = 0. The form is y=a(x−0)2−4=ax2−4y = a(x-0)^2 - 4 = ax^2 - 4. 2. Opens upward: This implies a>0a > 0. Choice A has a=1a=1. Choice B is incorrect because it opens downward (a=−1a=-1). Choice C is incorrect because vertex is (4,0)(4, 0). Choice D is incorrect because vertex is (0,4)(0, 4).

Key Steps:

•

The correct answer is y=x2−4y = x^2 - 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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