Question

Write the equation of the parabola in vertex form. vertex (3,4), point (1. - 8)​

Answer 1

`~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{`

`\begin{cases} h=3\\ k=4 \end{cases}\implies y=a(x-3)^2 + 4\hspace{5em}\textit{we also know that} \begin{cases} x=1\\ y=-8 \end{cases} \\\\\\ -8=a(1-3)^2 + 4\implies -12=a(-2)^2\implies \cfrac{-12}{(-2)^2}=a\implies -3=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y-3(x-3)^2 + 4 \end{array}}~\hfill`