Let a, h, and k be arbitrary real numbers with a0, 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. An extreme value occurs at the point (h,k). B. The graph of y=f(x) is a line. C. The graph of y=f(x) is a parabola. D. If a>0, then f has a global maximum. E. If a>0, then f has a global minimum. F. The maximum value of f(x) is h. 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. maximum B. minimum C. neither