Answer
$y=x^2-4x+2$
Work Step by Step
$y=ax^2+bx+c,$ $(1,-1),(3,-1),(-2,14)$
$\begin{cases}a+b+c=-1\\
9a+3b+c=-1\\
4a-2b+c=14
\end{cases}$
Multiplying the first equation by $2$ and adding it to the third equation.
$\begin{cases}2a+2b+2c=-2\\
4a-2b+c=14\\
-- -- -- -- \\
6a+3c=12
\end{cases}$
After simplifying the result becomes, $2a+c=4$
Multiplying the first equation by -3 and adding it to the second equation.
$\begin{cases}-3a-3b-3c=3\\
9a+3b+c=-1\\
-- -- -- --\\
6a-2c=2,
\end{cases}$
After simplifying the result becomes, $3a-c=1$
Adding the result together.
$\begin{cases}2a+c=4\\
3a-c=1\\
-- -- --\\
5a=5
\end{cases}$
Thus, $a=1, b=-4, c=2.$
Therefore, $y=x^2-4x+2$
