Question

What is the equation written in vertex form of a parabola with a vertex of (-5, -4) that passes through (-7, 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=-5\\ k=-4 \end{cases}\implies y=a( ~~ x-(-5) ~~ )^2 +(-4)\implies y=a(x+5)^2-4 \\\\\\ \textit{we also know that} \begin{cases} x=-7\\ y=8 \end{cases}\implies 8=a(-7+5)^2-4 \\\\\\ 12=a(-2)^2\implies 12=4a\implies \cfrac{12}{4}=a\implies 3=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=3(x+5)^2-4 \end{array}} ~\hfill`