g(x) is shown in the figure, which is a quadratic function opening downward with a vertex of (-5,6). f(x)=4x^2-108. Do the functions have the same concavity, f(x) and g(x)?
Choices:
A:Yes, $f$ and $g$ are both concave down.
B:Yes, $f$ and $g$ are both concave up.
C:No, $f$ is concave up and $g$ is concave down.
D:No, $f$ is concave down and $g$ is concave up.
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 (-5,6). f(x)=4x^2-108. Do the functions have the same concavity, f(x) and g(x)?
Choices:
A:Yes, $f$ and $g$ are both concave down.
B:Yes, $f$ and $g$ are both concave up.
C:No, $f$ is concave up and $g$ is concave down.
D:No, $f$ is concave down and $g$ is concave up.
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 (-5,6). f(x)=4x^2-108. Do the functions have the same concavity, f(x) and g(x)?
Choices:
A:Yes, $f$ and $g$ are both concave down.
B:Yes, $f$ and $g$ are both concave up.
C:No, $f$ is concave up and $g$ is concave down.
D:No, $f$ is concave down and $g$ is concave up.