f(x)= x²(x - 2)(x - 1)

Graph the polynomial functions.

Get the x intercepts by setting the
right side = 0

There is a double-zero (double root)
at x=0, which tells us that the graph 
is tangent to the x-axis at 0.

There are single zeros (single roots)
at x = 2 and x = 1. 

 x | y
-------
 0 | 0 (tangent at the origin) 
 1 | 0 (crosses the x-axis) 
 2 | 0 (crosses the x-axis)

Now we need to get some more points.
We need to get one point by choosing
x left of 0, another point by choosing
x between 0 and 1, another between 1
and 2 and one more right of 2.

 x | y
-------
 0 | 0 (tangent at the origin) 
 1 | 0 (crosses the x-axis) 
 2 | 0 (crosses the x-axis)
-1 | 6
.5 | .1875
1.5|-.5625
2.5|4.6875



Edwin