Nonlinear functions SAT question

Choice A is correct. The graph of a quadratic equation in the form $y=a{(x-h)}^2+k$, where $a$, $h$, and $k$ are positive constants, is a parabola that opens upward with vertex $(h,k)$. The given function $f(x)=\frac{1}{9}{(x-7)}^2+3$ is in the form $y=a{(x-h)}^2+k$, where $y=f(x)$, $a=\frac{1}{9}$, $h=7$, and $k=3$. Therefore, the graph of $y=f(x)$ is a parabola that opens upward with vertex $(7,3)$. Since the parabola opens upward, the vertex is the lowest point on the graph. It follows that the y-coordinate of the vertex of the graph of $y=f(x)$ is the minimum value of $f(x)$. Therefore, the minimum value of $f(x)$ is $3$. It’s given that $f(x)=\frac{1}{9}{(x-7)}^2+3$ represents the metal ball’s height above the ground, in inches, $x$ seconds after it started moving on a track. Therefore, the best interpretation of the vertex of the graph of $y=f(x)$ is that the metal ball’s minimum height was $3$ inches above the ground.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.