$f(x)$ 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

A monic polynomial is a polynomial where the cofficient of the highest order term is 1. (I didn't know this until now, I had to look it up here.)

 

f(x) is a monic polynomial with a degree of 2.   So we can say...

 

f(x)    =    1x²  + bx + c    =    x² + bx + c

 

The problem says  f(0) = 4 . So...

 

f(0)  =  0² + b(0) + c

  4   =  0   +   0   + c

  4   =  c

 

Now that we know  c = 4 , we know that  f(x) = x² + bx + 4 .

 

The problem says f(1) = 10 . So...

 

f(1)  =  1² + b(1) + 4

10   =  1  +   b   + 4

10   =  5 + b

  5   =  b

 

Now we know  b = 5  and  c = 4 , so   f(x)  =  x² + 5x + 4 .