[tex]\bf ~~~~~~\textit{parabola vertex form}
\\\\
\begin{array}{llll}
\boxed{y=a(x- h)^2+ k}\\\\
x=a(y- k)^2+ h
\end{array}
\qquad\qquad
vertex~~(\stackrel{}{ h},\stackrel{}{ k})\\\\
-------------------------------\\\\
vertex~(-3,4)\quad
\begin{cases}
x=-3\\
y=4
\end{cases}\implies \stackrel{f(x)}{y}=a[x-(-3)]^2+4
\\\\\\
y=a(x+3)^2+4
\\\\\\
\textit{we also know that }(-1,0)\quad
\begin{cases}
x=-1\\
y=0
\end{cases}\implies 0=a(-1+3)^2+4
\\\\\\
-4=4a\implies -1=a\qquad therefore\qquad y=-(x+3)^2+4[/tex]
