## Precalculus (6th Edition) Blitzer

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