Question 912267
Polynomial equation in factored form.
x-intercepts are readable directly from the factors:  -2, 1, 6.
y-intercept is y where x=0.  {{{y=(1/6)(2^3)(-1)^2(6)}}}, {{{y=8}}}.


Do no confuse polynomial functions with rational functions!  You say you understand that the equation has no asymptotes.  A polynomial function is defined for all x values and is continuous everywhere.  A rational function will have an expression of x in the denominator, and this causes some effect (in some cases) on sign of the function and also forces either a missing value for y or a vertical asymptote.


How to Graph:
The roots or x-intercepts make specific intervals on the x-axis.  The graph will either touch or cross the x axis at the roots.  Check the sign of y for each interval to know if that interval has positive y values or negative y values; and this helps you to sketch the graph.


Something is wrong with this graph....
{{{graph(300,300,-6,7,-10,10,(1/6)(x+2)^3(x-1)^2(6-x))}}}
The graph seems to be displaying wrongly.