Associated radius of convergence for a Taylor series

Question

Given the function $f(x) = 9x - 3x^3$ centered at $a = -2$, I found the Taylor series to be equal to

$6 − 27(x + 2) + 18(x + 2)^2 − 3(x + 2)^3$

I am confused on what the radius of convergence is. Would it not be at where it is centered?

Apologies for any poor formatting.

Answer 1

Notice that your function is already in the form

$$f(x) = \sum_{k=0}^\infty a_k x^k$$

The radius of convergence should thus be apparent.