Answer
$y=-x^2+2x+3$
Work Step by Step
Let's note:
$y=ax^2+bx+c$
Substitute $(x,y)$ by $(-1,0),(1,4),(2,3)$ and write the system of equations:
$\begin{cases}
a(-1)^2+b(-1)+c=0\\
a(1)^2+b(1)+c=4\\
a(2)^2+b(2)+c=3
\end{cases}$
$\begin{cases}
a-b+c=0\\
a+b+c=4\\
4a+2b+c=3
\end{cases}$
Multiply Equation 1 by -1 and add it to Equation 2 and Equation 3:
$\begin{cases}
-a+b-c=0\\
a+b+c=4\\
4a+2b+c=3
\end{cases}$
$\begin{cases}
a+b+c-a+b-c=4+0\\
4a+2b+c-a+b-c=3+0
\end{cases}$
$\begin{cases}
2b=4\\
3a+3b=3
\end{cases}$
$\begin{cases}
b=2\\
3a+3(2)=3
\end{cases}$
$\begin{cases}
b=2\\
3a=-3
\end{cases}$
$\begin{cases}
b=2\\
a=-1
\end{cases}$
$a+b+c=4$
$-1+2+c=4$
$1+c=4$
$c=3$
The function is:
$y=-x^2+2x+3$
