[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~(\stackrel{h}{2},\stackrel{k}{7})\qquad y=a(x-2)^2+7
\\\\\\
\textit{we also know it passes through }(\stackrel{x}{-1},\stackrel{y}{3})\qquad 3=a(-1-2)^2+7
\\\\\\
3=a(-3)^2+7\implies 3=a9+7\implies -4=9a\implies \cfrac{-4}{9}=a
\\\\\\
therefore\qquad \boxed{y=-\cfrac{4}{9}(x-2)^2+7}[/tex]
