Answer
$y=-\frac{1}{3}x^2-\frac{2}{3}x+1$
Work Step by Step
1. Based on the given conditions, form a system of equations
$\begin{cases} c=1 \\ a+b+c=0 \\ 4a-2b+c=1 \end{cases}$
2. Replace $c$ with 1 to get
$\begin{cases} a+b=-1 \\ 4a-2b=0 \end{cases}$ or
$\begin{cases} a+b=-1 \\ 2a-b=0 \end{cases}$
3. Add the two equations to get $3a=-1$, thus $a=-\frac{1}{3}$ and $b=-\frac{2}{3}$
4. We have $y=-\frac{1}{3}x^2-\frac{2}{3}x+1$
