Answer
$a=\frac{5}{3},$ $b=-1,$ $c=-\frac{14}{3}$
Work Step by Step
$y=ax^2+bx+x,$ $(-1,-2),(1,-4),(2,4)$
$\begin{cases}a-b+c=-2\\
a+b+c=-4\\
4a+2b+c=4
\end{cases}$
Multiplying the first equation by $-1$ and adding it to the fisrt equation.
$\begin{cases}-a+b-c=2\\
a+b+c=-4\\
-- -- -- --\\
2b=-2
\end{cases}$
$b=-1$.
Thus, replacing $b$ in the second equation by $-1$ and multiplying by $-1$.
$\begin{cases}-a-c=3\\
4a+c=2\\
-- -- --\\
3a=5
\end{cases}$
$a=\frac{5}{3}$ and $c=-\frac{14}{3}$
