#### Answer

$y=-x^2+2x+3$

#### Work Step by Step

Step 1. Based on the given conditions, we can set up the following system of equations:
$\begin{cases} a-b+c=0 \\ a+b+c=4 \\ 4a+2b+c=3 \end{cases}$
Step 2. Taking the difference between the first two equations, we have $2b=4$ and $b=2$
Step 3. With the know $b$, we have
$\begin{cases} a+c=2 \\ 4a+c=-1 \end{cases}$
Step 4. Taking the difference between the two equations, we have $3a=-3$ and $a=-1$
Step 5. Thus, the solutions are $(-1,2,3)$ and the function is $y=-x^2+2x+3$