<PRE><B>Question 1100633</B>
&lt;br&gt;
For x^4-6x^3+9x^2&lt;br&gt;
A) use the coefficient test to determine the graph’s end behavior &lt;br&gt;
The degree of the polynomial is even, and the leading coefficient is positive, so the function value is going to positive infinity on both ends.&lt;br&gt;
B) Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.&lt;br&gt;
{{{x^4-6x^3+9x^2 = (x^2)(x^2-6x+9) = (x^2)(x-3)^2}}}
There are two double roots, at x=0 and x=3.  Since they are double roots, the graph just touches the x-axis at those points,&lt;br&gt;
Note the answers to parts A and B tell us that the function value is never negative.&lt;br&gt;
C) Find the y-intercept.&lt;br&gt;
Set x equal to 0; the function value is 0.  So the y-intercept is the origin.
(But we already knew that, because 0 is a root.)&lt;br&gt;
D) Determine whether the graph has y-axis symmetry, origin symmetry, or neither.&lt;br&gt;
It is a polynomial function with terms that are both even and odd powers, so it has neither y-axis symmetry nor origin symmetry.&lt;br&gt;
E) Find a few additional points and graph the function. Use the maximum number of turning points to check whether it is drawn correctly.&lt;br&gt;
I&#39;m not sure what the instructions are asking you to do here....&lt;br&gt;
Here is a graph:&lt;br&gt;&lt;br&gt;
{{{graph(300,300,-2,5,-20,80,(x^2)(x-3)^2)}}}</PRE>