8
advanced-math

Which function is symmetric about the y-axis?

A

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

B

y=(x1)2y = (x - 1)^2

C

y=x2+xy = x^2 + x

D

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

Correct Answer: A

Choice A is the correct answer. Symmetry about the y-axis means the function is even, i.e., f(x)=f(x)f(-x) = f(x). This happens when the vertex is on the y-axis (h=0h=0).

  • A: Vertex (0,2)(0, 2). Symmetric.
  • B: Vertex (1,0)(1, 0). Not symmetric.
  • C: Vertex (0.5,0.25)(-0.5, -0.25). Not symmetric.
  • D: Vertex (2,0)(-2, 0). Not symmetric.

Choice B is incorrect because it is shifted right. Choice C is incorrect because it has a linear term. Choice D is incorrect because it is shifted left.