$f(x)$ 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.

michaelcai
Sep 16, 2017

#1**+2 **

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) = 1x^{2} + bx + c = x^{2} + bx + c

The problem says f(0) = 4 . So...

f(0) = 0^{2} + b(0) + c

4 = 0 + 0 + c

4 = c

Now that we know c = 4 , we know that f(x) = x^{2} + bx + 4 .

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

f(1) = 1^{2} + b(1) + 4

10 = 1 + b + 4

10 = 5 + b

5 = b

Now we know b = 5 and c = 4 , so f(x) = x^{2} + 5x + 4 .

hectictar
Sep 16, 2017

#1**+2 **

Best Answer

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) = 1x^{2} + bx + c = x^{2} + bx + c

The problem says f(0) = 4 . So...

f(0) = 0^{2} + b(0) + c

4 = 0 + 0 + c

4 = c

Now that we know c = 4 , we know that f(x) = x^{2} + bx + 4 .

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

f(1) = 1^{2} + b(1) + 4

10 = 1 + b + 4

10 = 5 + b

5 = b

Now we know b = 5 and c = 4 , so f(x) = x^{2} + 5x + 4 .

hectictar
Sep 16, 2017