Question

The vertex is (2,-7) and the y intercept is -3 what is the quadratic function

Answer 1

`\bf ~~~~~~\textit{parabola vertex form} \\\\ y=a(x- h)^2+ k \qquad\qquad vertex~~(\stackrel{2}{ h},\stackrel{-7}{ k}) \\\\\\ y=a(x-2)^2-7~\hspace{4em}\stackrel{\textit{y-intercept}}{(0, -3)}~~ \begin{cases} x=0\\ y=-3 \end{cases}\implies -3=a(0-2)^2-7 \\\\\\ 4=a(-2)^2\implies 4=4a\implies \cfrac{4}{4}=a\implies 1=a~\hfill y=1(x-2)^2-7 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y(x-2)^2-7~\hfill`