### 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: I know that a monic polynomial is one whose leading coefficient is $1$, so I can write $f(x)=x^2+bx+c$.
I also know that $f(0)=4$ and $f(1)=10$, so I can plug in those values of $x$ and get two equations for $b$ and $c$.
For $x=0$, I get $f(0)=0^2+b(0)+c=4$, which simplifies to $c=4$.
For $x=1$, I get $f(1)=1^2+b(1)+c=10$, which simplifies to $b+c=9$.
Since I already know that $c=4$, I can substitute that into the second equation and solve for $b$.
I get $b+4=9$, which implies $b=5$.