The vertex form equation of a parabola is:
\[ y=\frac{(x-h)^2}{4p} + k\]
The axis of symmetry here is at \(x=h\). The standard form equation of a parabola is:
\[ y= ax^2 + b x + c\]
Let's find the axis of symmetry here in terms of \(a\) and \(b\). We can express \(a\) and \(b\) in terms of \(h\) and \(p\):
\[ a=\frac{1}{4p} \quad b=\frac{-h}{2p} \]
This means:
\[\begin{gather} b=\frac{-2h}{4p} = -2ha \\ h = -\frac{b}{2a}\end{gather} \]
This means the axis of symmetry lies at \(x = -\frac{b}{a}\).