[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}{3})\implies y=a(x-2)^2+3
\\\\\\
\textit{we also know that }(\stackrel{x}{1}~~,~~\stackrel{y}{-1})\implies \underline{-1}=a(\underline{1}-2)^2+3
\\\\\\
-1=a(-1)^2+3\implies -1=a+3\implies -4=a
\\\\\\
\boxed{y=-4(x-2)^2+3}[/tex]
