Question 49111
Given the parabola y-2 = a(x-3)^2 goes through the point (2, 0), this means that algebraically, if you plug in x = 2 and y = 0, then the equation will be true (the left side will equal the right side).  Therefore, to find the value of "a", plug in x = 2 and y = 0 and then just solve for "a"

y-2 = a(x-3)^2
0-2 = a(2-3)^2
-2 = a(-1)^2
-2 = a(1) since (-1)^2 = 1
-2 = a  since a(1) = a

So the value of a needed to make the parabola y-2 = a(x-3)^2 pass through the point (2, 0) is a = -2

Remember - the key here is to know that if a given point "lies on a graph", the the values of the point plugged into the equaiont for the graph makes the left side equal to the right side when both are evaluated!