What is the range of f(x) = -(x-2)² + 9?

The function $-(x-2)^2+9$ is a parabola with vertex $(2,9)$. The leading coefficient is $-1$, so it opens downward and $9$ is the maximum output. Every output is at most $9$, so the range is $y\le9$, choice A. Choice B ($y\ge9$) reverses the inequality, which would hold for a parabola opening upward. Choice C ($x\le2$) describes inputs, but the range is about outputs, and the function accepts every real $x$ anyway. Choice D claims every real number can be an output, but $y=10$, for example, would require $(x-2)^2=-1$, which is impossible.