Answer
$y=-2x^2+x+3$
Work Step by Step
$y=ax^2+bx+c,$ $(1,2),(-2,-7),(2,-3)$
$\begin{cases} a+b+c=2\\
4a-2b+c=-7\\
4a+2b+c=-3
\end{cases}$
Multiplying the third equation by $-1$ and adding it to the first equation.
$\begin{cases}4a-2b+c=-7\\
-4a-2b-c=3\\
-- -- -- -- --\\
-4b=-4
\end{cases}$
$b=1$ and,
Multiplying the first equation and adding it to third equation.
$\begin{cases}-a-c=-1\\
4a+c=-5\\
-- -- -- --\\
3a=-6
\end{cases}$
$a=-2, b=1, c=3$
Therefore,
$y=-2x^2+x+3,$
