question: g(x) is shown in the figure, which is a quadratic function opening upward with a vertex of (3,−8) and a minimum value of -8. f(x)=x^2-2x+1. Which function has a greater y-intercept, f(x) or g(x)?
  Choices:
  A:$f$ has a greater $y$-intercept than $g$.
  B:$g$ has a greater $y$-intercept than $f$.
  C:$f$ and $g$ share the same $y$-intercept.
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 upward with a vertex of (3,−8) and a minimum value of -8. f(x)=x^2-2x+1. Which function has a greater y-intercept, f(x) or g(x)?
  Choices:
  A:$f$ has a greater $y$-intercept than $g$.
  B:$g$ has a greater $y$-intercept than $f$.
  C:$f$ and $g$ share the same $y$-intercept.
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 upward with a vertex of (3,−8) and a minimum value of -8. f(x)=x^2-2x+1. Which function has a greater y-intercept, f(x) or g(x)?
  Choices:
  A:$f$ has a greater $y$-intercept than $g$.
  B:$g$ has a greater $y$-intercept than $f$.
  C:$f$ and $g$ share the same $y$-intercept.
question_for_eval: g(x) is shown in the figure, which is a quadratic function opening upward with a vertex of (3,−8) and a minimum value of -8. f(x)=x^2-2x+1. Which function has a greater y-intercept, f(x) or g(x)?
  Choices:
  A:$f$ has a greater $y$-intercept than $g$.
  B:$g$ has a greater $y$-intercept than $f$.
  C:$f$ and $g$ share the same $y$-intercept.