Question

What is the equation in vertex

Answer 1

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Answer 2

$\bf ~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{ope ns~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \stackrel{\textit{vertex}}{(3,-2)}~~ \begin{cases} h = 3\\ k = -2 \end{cases}\implies y=a(x-3)^2-2 \\\\\\ \stackrel{\textit{passes through}}{(5,-1)}~~ \begin{cases} x=5\\ y= -1 \end{cases}\implies -1=a(5-3)^2-2\implies 1=a(2)^2 \\\\\\ 1=4a\implies \cfrac{1}{4}=a~\hfill \boxed{y=\cfrac{1}{4}(x-3)^2-2}$