On what interval is f(x) = (x-2)² + 3 decreasing?

The function $(x-2)^2+3$ is an upward-opening parabola with its vertex at $(2,3)$. To the left of the vertex, the outputs decrease as $x$ increases toward $2$; to the right, they increase. So the function is decreasing for $x<2$, choice A. Choice B ($x>2$) is the interval where it is increasing. Choices C and D use $3$, which is the $y$-coordinate of the vertex, not its $x$-coordinate. Intervals of increase and decrease are described by inputs, so the boundary must be $x=2$.