document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086965>Question 1086965</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.\r<BR>\n" );
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document.write( "f(x) = -x^3(x + 2)^2(x - 6)<BR>\n" );
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document.write( "origin symmetry<BR>\n" );
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document.write( "y-axis symmetry<BR>\n" );
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document.write( "neither </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #701225 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=701225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+-x%5E3%28x+%2B+2%29%5E2%28x+-+6%29 ALIGN=MIDDLE  ALT=\"f%28x%29+=+-x%5E3%28x+%2B+2%29%5E2%28x+-+6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the graph will be symmetrical with respect to the y-axis if:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-x%29+=+f%28x%29 ALIGN=MIDDLE  ALT=\"f%28-x%29+=+f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-x%29+=+f%28x%29 ALIGN=MIDDLE  ALT=\"f%28-x%29+=+f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >......if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=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=f%28-1%29+=+f%281%29 ALIGN=MIDDLE  ALT=\"f%28-1%29+=+f%281%29\"   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=+%28-%28-1%29%5E3%29%28-1+%2B+2%29%5E2%28-1-6%29=-1%5E3%281+%2B+2%29%5E2%281-6%29 ALIGN=MIDDLE  ALT=\"+%28-%28-1%29%5E3%29%28-1+%2B+2%29%5E2%28-1-6%29=-1%5E3%281+%2B+2%29%5E2%281-6%29\"   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=+-%28-1%29%281%29%5E2%28-7%29=-1%283%29%5E2%28+-5%29 ALIGN=MIDDLE  ALT=\"+-%28-1%29%281%29%5E2%28-7%29=-1%283%29%5E2%28+-5%29\"   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=+1%281%29%28-7%29=-1%289%29%28+-+5%29 ALIGN=MIDDLE  ALT=\"+1%281%29%28-7%29=-1%289%29%28+-+5%29\"   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=+-7%3C%3E45 ALIGN=MIDDLE  ALT=\"+-7%3C%3E45\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>the graph is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > symmetrical with respect to the y-axis\r<BR>\n" );
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document.write( "the graph will be symmetrical with respect to the origin if:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-x%29+=+-f%28x%29 ALIGN=MIDDLE  ALT=\"f%28-x%29+=+-f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >......if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=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=f%28-1%29+=+f%281%29 ALIGN=MIDDLE  ALT=\"f%28-1%29+=+f%281%29\"   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=+-%28-1%29%5E3%28-1+%2B+2%29%5E2%28-1+-+6%29=-1%5E3%281+%2B+2%29%5E2%281+-+6%29 ALIGN=MIDDLE  ALT=\"+-%28-1%29%5E3%28-1+%2B+2%29%5E2%28-1+-+6%29=-1%5E3%281+%2B+2%29%5E2%281+-+6%29\"   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=+-%28-1%29%281%29%5E2%28-7%29=-%28-1%283%29%5E2%28+-+5%29%29 ALIGN=MIDDLE  ALT=\"+-%28-1%29%281%29%5E2%28-7%29=-%28-1%283%29%5E2%28+-+5%29%29\"   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=+1%281%29%28-7%29=-%28-1%289%29%28+-+5%29%29 ALIGN=MIDDLE  ALT=\"+1%281%29%28-7%29=-%28-1%289%29%28+-+5%29%29\"   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=+-7%3C%3E-45 ALIGN=MIDDLE  ALT=\"+-7%3C%3E-45\"   DISABLED_style= \"max-width:90%; height:auto;\" >=>the graph is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > symmetrical with respect to the origin\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+-20%2C+20%2C+-20%2C+20%2C+-x%5E3%28x+%2B+2%29%5E2%2A%28x+-+6%29%2C-x%5E6%2B2x%5E5%2B20x%5E4%2B+24x%5E3%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=neither ALIGN=MIDDLE  ALT=\"neither\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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