Question

A parabola opening up or down has vertex (1, 4) and passes through (19, -65/4).

Write its

equation in vertex form.

Answer 1

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

`-\cfrac{65}{4}=a(19-1)^2 + 4\implies -\cfrac{65}{4}-4=a(18)^2\implies -\cfrac{80}{4}=324a \\\\\\ -20=324a\implies \cfrac{-20}{324}=a\implies -\cfrac{5}{81}=a~\hfill \boxed{y= -\cfrac{5}{81}(x-1)^2 + 4}`