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.
A monic polynomial is one where the lead coefficient on the x^2 term is 1
We have the form f(x) = x^2 + bx + c
If (0) = 4 then c =4
And we have that f(1) = 10 .....which means that
(1)^2 + b(1) + 4 = 10
5 + b = 10
b = 5
So
f(x) = 1x^2 + 5x + 4