Let $a$, $h$, and $k$ be arbitrary real numbers with $a\neq 0$, and let $f$ be the function given by the rule $f(x)=a(x-h)^2+k$.

Which of the following statements are true about $f$? Select all that apply.

A. If $a>0$, then $f$ has a global maximum.

B. The maximum value of $f(x)$ is $h$.

C. If $a>0$, then $f$ has a global minimum.

D. An extreme value occurs at the point $(h,k)$.

E. The graph of $y=f(x)$ is a parabola.

F. The graph of $y=f(x)$ is a line.

G. None of the above

Next we use some calculus to develop familiar ideas from a different perspective. To start, treat $a$, $h$, and $k$ as constants and compute $f'(x)$.
$f'(x) =$

Find a critical value of $f$. (This will depend on at least one of $a$, $h$, and $k$.)
Critical value =

Assume that $a<0$. Make a derivative sign chart for $f$. Based on this information, classify the critical value of $f$ as a maximum or minimum.

A. minimum
B. maximum
C. neither