Chapter 6 - Matrices and Determinants - Exercise Set 6.1 - Page 600: 39

$-x^2+x+2$

Plugging in $x=-2$: $4a-2b+c=-4$. Plugging in $x=1$: $a+b+c=2$. Plugging in $x=2$: $4a+2b+c=0$. Subtracting the first equation from the second one we get $4b=4\\b=1$ Thus our equations: $a+1+c=2\\a+c=1$ and $4a+2(1)+c=0\\4a+c=-2$. Thus here subtracting the first from the second we get: $3a=-3\\a=-1$ $a+c=1\\c=1-a=1-(-1)=2$ Thus $f(x)=-x^2+x+2$