Let $f(x)$ be a monic polynomial such that $f(0)=4$ and $f(1)=8$. If $f(x)$ has degree $2$, what is $f(x)$? Enter your answer in the form $ax^2+bx+c$, where $a$, $b$, and $c$ are real numbers.
We have
a*0^2 + b*0 + c = 4 so c = 4
and
a*1^2 + b*1 + 4 = 8
a + b = 4
Since it is monic a = 1 and b =3
So
f(x) = x^2 + 3x + 4
+816 
