[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{-2}{ h},\stackrel{-3}{ k})\\\\
-------------------------------\\\\
\begin{cases}
h=-2\\
k=-3
\end{cases}\implies y=a[x-(-2)]^2-3\implies y=a(x+2)^2-3
\\\\\\
\textit{we also know that }
\begin{cases}
x=4\\
y=1
\end{cases}\implies 1=a(4+2)^2-3
\\\\\\
4=36a\implies \cfrac{4}{36}=a\implies \cfrac{1}{9}=a
\\\\\\
therefore\qquad \boxed{y=\cfrac{1}{9}(x+2)^2-3}[/tex]
[tex]\bf y=\cfrac{1}{9}(x+2)^2-3\implies y=\cfrac{1}{9}(x^2+4x+4)-3
\\\\\\
y=\cfrac{1}{9}x^2+\cfrac{4}{9}x+\cfrac{4}{9}-3\implies \stackrel{standard~form}{y=\cfrac{1}{9}x^2+\cfrac{4}{9}x-\cfrac{23}{9}}[/tex]
