document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1013092>Question 1013092</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4.2\r<BR>\n" );
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document.write( "Find the zeros for the given polynomial function and give the multiplicity for each zero. State whether <BR>\n" );
document.write( "the graph crosses the x-axis or touches the x-axis and turns around at each zero.\r<BR>\n" );
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document.write( "f(x)=x^3 -12x^2+36x\r<BR>\n" );
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document.write( "The zeros are:\r<BR>\n" );
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document.write( "The multiplicity at the leftmost zero is:\r<BR>\n" );
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document.write( "The multiplicity at the rightmost zero is:\r<BR>\n" );
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document.write( "Does the graph (on the leftmost zero) cross the x-axis or touch the x-axis and turn around:\r<BR>\n" );
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document.write( "Does the graph (on the rightmost zero) cross the x-axis or touch the x-axis and turn around: </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #629301 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=629301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the zeros for the given polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around at each zero.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3+-12x%5E2%2B36x ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3+-12x%5E2%2B36x\"   DISABLED_style= \"max-width:90%; height:auto;\" >....set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=0 ALIGN=MIDDLE  ALT=\"f%28x%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3+-12x%5E2%2B36x=0 ALIGN=MIDDLE  ALT=\"x%5E3+-12x%5E2%2B36x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%5E2+-12x%2B36%29=0 ALIGN=MIDDLE  ALT=\"x%28x%5E2+-12x%2B36%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x%5E2+-12x%2B6%5E2%29=0 ALIGN=MIDDLE  ALT=\"x%28x%5E2+-12x%2B6%5E2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-6%29%5E2++=+0 ALIGN=MIDDLE  ALT=\"x%28x-6%29%5E2++=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The zeros are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0 ALIGN=MIDDLE  ALT=\"x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The multiplicity at the leftmost zero is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-6%29%5E2++=+0 ALIGN=MIDDLE  ALT=\"%28x-6%29%5E2++=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-6++=+0 ALIGN=MIDDLE  ALT=\"x-6++=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The multiplicity at the rightmost zero is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-5%2C15%2C+-10%2C+10%2C+x%5E3+-12x%5E2%2B36x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-5%2C15%2C+-10%2C+10%2C+x%5E3+-12x%5E2%2B36x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Does the graph (on the leftmost zero) cross the x-axis or touch the x-axis and turn around:<BR>\n" );
document.write( "the graph cross the x-axis\r<BR>\n" );
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document.write( "Does the graph (on the rightmost zero) cross the x-axis or touch the x-axis and turn around: \r<BR>\n" );
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document.write( "the graph touch the x-axis and turn around\r<BR>\n" );
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document.write( " </SPAN>\n" );
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