Question

PLEASE SOMEONE HELP ME. Use the given values to write a quadratic equation of the form f(x)=ax^2+bx+c:

Answer 1

C)

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

$\bf \stackrel{vertex}{(2,-3)}~~ \begin{cases} h=2\\ k=-3 \end{cases}\implies y = a(x-2)^2-3 \\\\\\ \stackrel{passes~through}{(4,-1)}~~ \begin{cases} x=4\\ y=-1 \end{cases}\implies -1=a(4-2)^2-3\implies 2=a(4-2)^2 \\\\\\ 2=a(2)^2\implies 2=4a\implies \cfrac{2}{4}=a\implies \cfrac{1}{2}=a \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=\cfrac{1}{2}(x-2)^2-3~\hfill$