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.
query_wo: 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.
query_cot: 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.
question_for_eval: 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.