Question

Write an equation of the parabola that passes through the point (-5,2) and has vertex (7,-2)

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=7\\ k=-2\\ \end{cases}\implies y=a(~~x-7~~)^2 + (-2)\hspace{4em}\textit{we also know that} \begin{cases} x=-5\\ y=2 \end{cases} \\\\\\ 2=a(-5-7)^2-2\implies 4=a(-12)^2\implies 4=144a\implies \cfrac{4}{144}=a \\\\\\ \cfrac{1}{36}=a\hspace{9em} {\Large \begin{array}{llll} y=\cfrac{1}{36}(x-7)^2-2 \end{array}}`

Check the picture below.