Question 86305
y= x(x-4)^2 has 2 zeros ; one at 0 and one at 4. The factor generating the one at 0 is x, which is raised to an odd power [1 by default since there's none specified]. So the graph will cross the x-axis at x = 0 [the origin]
The factor generating the one at 4 is x - 4, which is raised to an even power, 2. So the graph will touch but not cross the x-axis at x = 4.