Choice A is the correct answer. This equation is in the form $y = ax^2 + c$, where $b=0$.

1. Calculate x-coordinate: $x = -b/2a = -0/2(1) = 0$.
2. Calculate y-coordinate: $y = 0^2 + 2 = 2$.

Alternatively, recognize this as a vertical shift of the parent function $y=x^2$ up by 2 units. The vertex moves from $(0,0)$ to $(0,2)$.

Choice B is incorrect because it swaps x and y. Choice C is incorrect because it ignores the constant term. Choice D is incorrect because it confuses horizontal and vertical shifts.