Question bank / Nonlinear functions

Math · Advanced MathEasy

Which statement about the graph of y=−(x−2)2+6y = -(x - 2)^2 + 6 in the xyxy-plane is true?

A

It has a maximum at (2,6)(2, 6).

B

It has a minimum at (2,6)(2, 6).

C

It has a maximum at (−2,6)(-2, 6).

D

It has a minimum at (−2,6)(-2, 6).

Show answer and explanation

Answer: A

The equation is in vertex form, y=a(x−h)2+ky = a(x - h)^2 + k, with vertex (h,k)=(2,6)(h, k) = (2, 6). Because a=−1a = -1 is negative, the parabola opens downward, so the vertex is a maximum.

Choice C reads (x−2)(x - 2) as giving h=−2h = -2, but the form (x−h)(x - h) means h=2h = 2.

Why the other choices are wrong

  • B. The coefficient of the squared term is -1, so the parabola opens downward and the vertex is a maximum.
  • C. In (x - 2)², the x-coordinate of the vertex is 2, not -2.
  • D. Both parts are off. The vertex is at x = 2, and a parabola that opens downward has a maximum.
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