Taylor Polynomial of degree 2

Question

Suppose g is a function which has continuous derivatives, and that$ g(8)=1,g′(8)=−1,g″(8)=−3$, and $g'''(8)=2 $

What is the Taylor polynomial of degree $2$ for $g$ near $8$?

I am relatively new to Taylor series, so it could be the way this question is worded, but I am not sure what the question is asking for. While I have come to this site several time before, this is my first post, so I apologize if I am not following all eligible rules.

Thanks

Answer 1

Hint:

The Taylor expansion of a given function $f(x)$ centered in a point $a\in D$, where $D$ is the domain of the function, is given by:

$$f(x)=\sum_{n=0}^\infty \frac{1}{n!}f^{(n)}(a)(x-a)^{n} $$ Where $f^{(n)}(a)$ is the $n$th derivative at the point of centering.

So I guess if you think what is the degree of a polynomial you can go on.