document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176413>Question 1176413</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For each polynomial function, describe or determine the following, then sketch the graph.<BR>\n" );
document.write( "A. Leading term<BR>\n" );
document.write( "B. X-intercept<BR>\n" );
document.write( "C. Y-intercept <BR>\n" );
document.write( "D. Multiplicity of roots<BR>\n" );
document.write( "E. Number of turning points <BR>\n" );
document.write( "F. Sketch\r<BR>\n" );
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document.write( "1.y=(x^2-5) (x-1)^2 (x-2)^2<BR>\n" );
document.write( "2.y=2x^4-3x^3-18x^2+6x+28 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #803312 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=803312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%5E2-5%29+%28x-1%29%5E2+%28x-2%29%5E2 ALIGN=MIDDLE  ALT=\"y=%28x%5E2-5%29+%28x-1%29%5E2+%28x-2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >....multiply and you will get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E6+-+6+x%5E5+%2B+8+x%5E4+%2B+18+x%5E3+-+61+x%5E2+%2B+60+x+-+20 ALIGN=MIDDLE  ALT=\"y=x%5E6+-+6+x%5E5+%2B+8+x%5E4+%2B+18+x%5E3+-+61+x%5E2+%2B+60+x+-+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A. Leading term  is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E6 ALIGN=MIDDLE  ALT=\"x%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B. X-intercept  are at x=sqrt(5), x=-sqrt(5),x=1,x=2<BR>\n" );
document.write( "C. Y-intercept is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-20 ALIGN=MIDDLE  ALT=\"-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "D. Multiplicity of roots:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%285%29+ ALIGN=MIDDLE  ALT=\"x=sqrt%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiplicity 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+-sqrt%285%29 ALIGN=MIDDLE  ALT=\"x=+-sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiplicity 1<BR>\n" );
document.write( "<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;\" > Multiplicity 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiplicity 2<BR>\n" );
document.write( "E. Number of turning points is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "note:<BR>\n" );
document.write( "A polynomial of degree <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >, will have a maximum of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+-1 ALIGN=MIDDLE  ALT=\"n+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > turning points.<BR>\n" );
document.write( "The total number of turning points for a polynomial with an even degree is an odd number.<BR>\n" );
document.write( "  example:  A polynomial with degree of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > can have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1 ALIGN=MIDDLE  ALT=\"+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > turning points<BR>\n" );
document.write( "The total number of points for a polynomial with an odd degree is an even number.<BR>\n" );
document.write( "   example:  A polynomial of degree <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > can have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2 ALIGN=MIDDLE  ALT=\"+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" > turning points (zero is an even number).\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "F. Sketch\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%2C+5%2C+-5%2C+5%2C+%28x%5E2-5%29%2A%28x-1%29%5E2%2A%28x-2%29%5E2%2C%28x%5E2-5%29%2A%28x-1%29%5E2%2A%28x-2%29%5E2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x%5E4-3x%5E3-18x%5E2%2B6x%2B28 ALIGN=MIDDLE  ALT=\"y=2x%5E4-3x%5E3-18x%5E2%2B6x%2B28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x+%2B+2%29+%282x+-+7%29+%28x%5E2+-+2%29 ALIGN=MIDDLE  ALT=\"y+=+%28x+%2B+2%29+%282x+-+7%29+%28x%5E2+-+2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "zeros: <BR>\n" );
document.write( "A. Leading term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E4 ALIGN=MIDDLE  ALT=\"2x%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "B. X-intercept are: <BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2C0 ALIGN=MIDDLE  ALT=\"-2%2C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F2%2C+%7B%7B%7B0 ALIGN=MIDDLE  ALT=\"7%2F2%2C+%7B%7B%7B0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2C+%7B%7B%7B0 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2C+%7B%7B%7B0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-sqrt%282%29%2C+%7B%7B%7B0 ALIGN=MIDDLE  ALT=\"+-sqrt%282%29%2C+%7B%7B%7B0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "C. Y-intercept is (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28 ALIGN=MIDDLE  ALT=\"28\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "D. Multiplicity of roots  <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2 ALIGN=MIDDLE  ALT=\"x=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiplicity of 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=7%2F2 ALIGN=MIDDLE  ALT=\"x=7%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Multiplicity of 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%282%29 ALIGN=MIDDLE  ALT=\"x=sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,Multiplicity of 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-sqrt%282%29 ALIGN=MIDDLE  ALT=\"x=-sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,Multiplicity of 1\r<BR>\n" );
document.write( "\n" );
document.write( "E. Number of turning points <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "F. Sketch\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+-10%2C+10%2C+-45%2C+35%2C+2x%5E4-3x%5E3-18x%5E2%2B6x%2B28%2C2x%5E4-3x%5E3-18x%5E2%2B6x%2B28%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );