Question

Write the equation of the parabola in vertex form.

Vertex (2,3) point (1,-1)

f(x)=

Answer 1

`\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \boxed{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k})\\\\ -------------------------------\\\\ vertex~(\stackrel{h}{2}~~,~~\stackrel{k}{3})\implies y=a(x-2)^2+3 \\\\\\ \textit{we also know that }(\stackrel{x}{1}~~,~~\stackrel{y}{-1})\implies \underline{-1}=a(\underline{1}-2)^2+3 \\\\\\ -1=a(-1)^2+3\implies -1=a+3\implies -4=a \\\\\\ \boxed{y=-4(x-2)^2+3}`