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
+4622 
