Question

The quadratic function that has a vertex of (9, -1) and passes through the point (7, 7) is:

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=9\\ k=-1\\ \end{cases}\implies y=a(~~x-9~~)^2 + (-1)\hspace{4em}\textit{we also know that} \begin{cases} x=7\\ y=7 \end{cases} \\\\\\ 7=a(7-9)^2 -1\implies 8=a(-2)^2\implies 8=4a\implies \cfrac{8}{4}=a\implies 2=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=2(x-9)^2 -1 \end{array}}~\hfill`