g(x) is shown in the figure, which is a quadratic function going through (0,7), (-4,7) with a vertex (-2,3). f(x)=4(x-5)^2+2. Which function has a greater minimum?
Choices:
A:$f$ has a greater minimum than $g$.
B:$g$ has a greater minimum than $f$.
C:$f$ and $g$ share the same minimum.
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 going through (0,7), (-4,7) with a vertex (-2,3). f(x)=4(x-5)^2+2. Which function has a greater minimum?
Choices:
A:$f$ has a greater minimum than $g$.
B:$g$ has a greater minimum than $f$.
C:$f$ and $g$ share the same minimum.
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 going through (0,7), (-4,7) with a vertex (-2,3). f(x)=4(x-5)^2+2. Which function has a greater minimum?
Choices:
A:$f$ has a greater minimum than $g$.
B:$g$ has a greater minimum than $f$.
C:$f$ and $g$ share the same minimum.