$$f(x)=ax^{2}+4x+c$$

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 \(f(-9)=f(3)\), which of the following must be true?

I. \(c<0\)

II. \(a\geq 1\)