These are all in vertex form,
y = a(x - p)² + q
When a is positive this makes a CUP (concave up positive) and has a minimum, not a maximum. When a is negative then the maximum is just when the squared term is 0, in which case
y = q
is the maximum.
From the figure g(x) has a maximum of 3 at x=2.
A. Positive coefficient, CUP, no max
B. CUP, no max
C. Negative coefficient, will have a max, at y=3, not greater than 3.
D. Negative coefficient, max at y=4
Answer: D
