g(x) is shown in the figure, which is a quadratic function opening downward with a vertex of (-8,8). f(x)=-5(x+4)^2+8. Which function has a greater maximum?
Choices:
A:$f$ has a greater maximum than $g$.
B:$g$ has a greater maximum than $f$.
C:$f$ and $g$ share the same maximum.
Please directly answer the question and provide the correct option letter, e.g., A, B, C, D.
Question: g(x) is shown in the figure, which is a quadratic function opening downward with a vertex of (-8,8). f(x)=-5(x+4)^2+8. Which function has a greater maximum?
Choices:
A:$f$ has a greater maximum than $g$.
B:$g$ has a greater maximum than $f$.
C:$f$ and $g$ share the same maximum.
Please first conduct reasoning, and then answer the question and provide the correct option letter, e.g., A, B, C, D, at the end.
Question: g(x) is shown in the figure, which is a quadratic function opening downward with a vertex of (-8,8). f(x)=-5(x+4)^2+8. Which function has a greater maximum?
Choices:
A:$f$ has a greater maximum than $g$.
B:$g$ has a greater maximum than $f$.
C:$f$ and $g$ share the same maximum.