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 has a lead coefficient of 1......so a = 1

And since f(0) = 4, then c = 4

So all we need to do is solve for b

f(1) = 10 .... so ......

(1)^2 + b(1) + 4 = 10

1 + b + 4 = 10

b = 5

So.....our function is

f(x) = x^2 + 5x + 4