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Math·Advanced Math·Nonlinear functions

hard

$f(x)=a{x}^2+2x+c$

In the given quadratic function, $a$ and $c$ are constants. The graph of $y=f(x)$ in the $xy$-plane is a parabola that opens upward and has a vertex at the point $(h,k)$ where $h$ and $k$ are constants.

If $k<0$ and $f(-5)=f(1)$, which of the following must be true?
I. $c<0$
II. $a\ge 1$

A

I only

B

II only

C

I and II

D

Neither I nor II