Question

Write an equation for each parabola.

Answer 1

`~~~~~~\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`

`\begin{cases} h=6\\ k=-23\\ \end{cases}\implies y=a(~~x-6~~)^2 + (-23)\hspace{4em}\textit{we also know that} \begin{cases} x=2\\ y=-375 \end{cases} \\\\\\ -375=a(2-6)^2 -23\implies -352=a(-4)^2\implies -352=16a \\\\\\ \cfrac{-352}{16}=a\implies -22=a\hspace{9em}\boxed{y=-22(x-6)^2 - 23}`

Check the picture below.