[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=3\\ k=-7 \end{cases}\implies y=a(x-3)^2-7\qquad \textit{we also know that} \begin{cases} x=1\\ y=-10 \end{cases} \\\\\\ -10=a(1-3)^2-7\implies -3=a(-2)^2\implies -3=4a\implies -\cfrac{3}{4}=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y=-\cfrac{3}{4}(x-3)^2-7~\hfill[/tex]
