10
advanced-math

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

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

Correct Answer: A

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).

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