3

Set 5: Quadratic Equations (Advanced)

Explanation

Answer: A

A parabola has vertex (−1,4)(-1, 4) and passes through (0,3)(0, 3). What is its equation?

A.

y=−(x+1)2+4y = -(x + 1)^2 + 4

✓ Correct
B.

y=(x+1)2+4y = (x + 1)^2 + 4

C.

y=−(x−1)2+4y = -(x - 1)^2 + 4

D.

y=−2(x+1)2+4y = -2(x + 1)^2 + 4

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Start with vertex form: y=a(x−h)2+ky = a(x - h)^2 + k. 1. Substitute vertex (−1,4)(-1, 4): y=a(x+1)2+4y = a(x + 1)^2 + 4. 2. Use point (0,3)(0, 3) to find aa: 3=a(0+1)2+43= a(0 + 1)^2 + 4. 3. Solve: 3=a+4⇒a=−13= a + 4 \Rightarrow a = -1. Equation: y=−(x+1)2+4y = -(x + 1)^2 + 4. Choice B is incorrect because a=1a=1 would pass through (0,5)(0, 5). Choice C is incorrect because vertex would be (1,4)(1, 4). Choice D is incorrect because a=−2a=-2 would pass through (0,2)(0, 2).

Key Steps:

•

The correct answer is y=−(x+1)2+4y = -(x + 1)^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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