parabola problems, and other questions

Hello, I have a few questions that are making my head hurt.

Question 1:

if the parabola $\displaystyle y -2=a(x-3)^2$ goes through the point (2,0), what is the value of a?

Question 2:

Given $\displaystyle x^3-4x^2+2x+1=0$

a:How many possible positive roots are there?

b:How many possible negative roots are there?

c:What are the possible negative roots?

d:Using synthetic substitution, which of the possible rational roots is actually a root of the equation?

e:Find the irrational roots of the equation.(Hint:Use the quadratic formula to solve the depressed equation.)

Thanks