Let $\displaystyle f(x) = \frac{x^{2}}{\left(x-2\right)^{2}}.$ Answer the following questions.

1. Find the vertical asymptote(s) of $f.$
Answer (separate by commas): $x =$

2. Find the horizontal asymptote(s) of $f.$
Answer (separate by commas): $y =$

3. Find the interval(s) on which $f$ is increasing.

4. Find the interval(s) on which $f$ is decreasing.
5. Find the local maxima of $f.$ List your answers as points in the form $(a,b)$.
6. Find the local minima of $f.$ List your answers as points in the form $(a,b)$.
7. Find the interval(s) on which $f$ is concave upward.
8. Find the interval(s) on which $f$ is concave downward.