Question

7. Write the equation using the given
information:
Vertex: (3,-2)
Point: (1, 2)

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=-2 \end{cases}\implies y=a(x-3)^2 -2\hspace{5em}\textit{we also know that} \begin{cases} x=1\\ y=2 \end{cases} \\\\\\ 2=a(1-3)^2 -2\implies 4=a(-2)^2\implies 4=4a\implies \cfrac{4}{4}=a\implies 1=a \\\\[-0.35em] ~\dotfill\\\\ y=1(x-3)^2 -2\implies {\Large \begin{array}{llll} y=(x-3)^2 -2 \end{array}}`