### 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: A monic polynomial is one whose leading coefficient is $1$.
So $f(x)$ has the form $x^2+bx+c$ for some real numbers $b$ and $c$.
Since $f(0)=4$, we can plug in $x=0$ and get $c=4$.
Since $f(1)=10$, we can plug in $x=1$ and get $1+b+4=10$, or $b=5$.
Therefore, $f(x)=x^2+5x+4$.