Question

Wite the equation of the parabola in vertex form :

Vertex : (2,2) , Point : (3,-2)

f(x) =_________________

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