document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100633>Question 1100633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For x^4-6x^3+9x^2<BR>\n" );
document.write( "A) use the coefficient test to determine the graph’s end behavior <BR>\n" );
document.write( "B) Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.<BR>\n" );
document.write( "C) Find the y-intercept.<BR>\n" );
document.write( "D) Determine whether the graph has y-axis symmetry, origin symmetry, or neither.<BR>\n" );
document.write( "E) Find a few additional points and graph the function. Use the maximum number of turning points to check whether it is drawn correctly. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #715185 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=715185\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "For x^4-6x^3+9x^2<br><BR>\n" );
document.write( "A) use the coefficient test to determine the graph’s end behavior <br><BR>\n" );
document.write( "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.<br><BR>\n" );
document.write( "B) Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4-6x%5E3%2B9x%5E2+=+%28x%5E2%29%28x%5E2-6x%2B9%29+=+%28x%5E2%29%28x-3%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E4-6x%5E3%2B9x%5E2+=+%28x%5E2%29%28x%5E2-6x%2B9%29+=+%28x%5E2%29%28x-3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "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,<br><BR>\n" );
document.write( "Note the answers to parts A and B tell us that the function value is never negative.<br><BR>\n" );
document.write( "C) Find the y-intercept.<br><BR>\n" );
document.write( "Set x equal to 0; the function value is 0.  So the y-intercept is the origin.<BR>\n" );
document.write( "(But we already knew that, because 0 is a root.)<br><BR>\n" );
document.write( "D) Determine whether the graph has y-axis symmetry, origin symmetry, or neither.<br><BR>\n" );
document.write( "It is a polynomial function with terms that are both even and odd powers, so it has neither y-axis symmetry nor origin symmetry.<br><BR>\n" );
document.write( "E) Find a few additional points and graph the function. Use the maximum number of turning points to check whether it is drawn correctly.<br><BR>\n" );
document.write( "I'm not sure what the instructions are asking you to do here....<br><BR>\n" );
document.write( "Here is a graph:<br><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28300%2C300%2C-2%2C5%2C-20%2C80%2C%28x%5E2%29%28x-3%29%5E2%29 ALIGN=MIDDLE  ALT=\"graph%28300%2C300%2C-2%2C5%2C-20%2C80%2C%28x%5E2%29%28x-3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );