Question

Equation of a parabola that passes through (8,3) and has a vertex of (4,-1)

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=4\\ k=-1\\ \end{cases}\implies y=a(~~x-4~~)^2 + (-1)\hspace{4em}\textit{we also know that} \begin{cases} x=8\\ y=3 \end{cases} \\\\\\ 3=a(8-4)^2 -1\implies 4=16a\implies \cfrac{4}{16}=a\implies \cfrac{1}{4}=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=\cfrac{1}{4}(x-4)^2 -1 \end{array}} ~\hfill`