Remark
If you start with the graph y = x^3 - x^2, it will cross the x axis at (0,0). The y intercept for that graph is when x = 0. Thus y = 0^3 - 0^2 = 0 when x = 0 and that 's how you derive (0,0)
Remark 2
Now watch that point (0,0) on the left graph below when you change it to y = (x - 2)^3 - (x - 2)^2 [Never mind the 3 for now. We'll deal with it later on]. Notice that what is happening at (2,0) is what is happening with the blue graph as compared to the red one. The change is very dramatic. Instead of going up, both graphs start to go down at the points I'm telling you to watch.
Conclusion 1.
So the first prediction you should make is that the - 2 forces the graph to move 2 units to the right.
Remark 3
What about the three on the right hand side? It is easier if you rewrite the equation as y = (x-2)^3 - (x -2)^ - 3. That means you have subtracted three from the right side. That should move (2,0) down 3 units. (minus is down when a number is on the right.) The green line in the right graph shows you that.
Conclusion 2
The green line shows you the final movement. (0,0) goes 3 units down and 2 units right. The new point we have been watching is (2,3)
