### Instruction: $f(x)$ is a monic polynomial such that $f(0)=4$ and $f(1)=10$. If $f(x)$ has degree $2$, what is $f(x)$? Express your answer in the form $ax^2+bx+c$, where $a$, $b$, and $c$ are real numbers.### Response: Let $f(x)=ax^2+bx+c$.
We know that $f(0)=4$, so $a(0)^2+b(0)+c=4$.
That gives us $c=4$. So $f(x)=ax^2+bx+4$.
We also know that $f(1)=10$, so $a(1)^2+b(1)+4=10$.
That gives us $a+b=6$.
And we know that $f(x)$ is monic, so $a=1$.
That means $b=5$.