document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190248>Question 190248</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there, I was doing my Advanced functions homework and have been stuck with this question for about an hour now, I would really appreciate if someone could help me with this.\r<BR>\n" );
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document.write( "Determine an equation of a polynomial function with zeros at x= 2, -2, 1, and y-intercept of 24.\r<BR>\n" );
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document.write( "Once again, I could really use the help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142764 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=142764\">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=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <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;\" >, or <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;\" > Start with the given solutions\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-2=0 ALIGN=MIDDLE  ALT=\"x-2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B2=0 ALIGN=MIDDLE  ALT=\"x%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1=0 ALIGN=MIDDLE  ALT=\"x-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get every term to the left side\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x%2B2%29%28x-1%29=0 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x%2B2%29%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the equations to form on equation. (use the zero product property)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x-2%29%28x%2B2%29%28x-1%29=0 ALIGN=MIDDLE  ALT=\"a%28x-2%29%28x%2B2%29%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Append an \"a\" (a constant) to the beginning of the left side. This constant will allow us to force the graph to go through the y-intercept of 24.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x%5E2-4%29%28x-1%29=0 ALIGN=MIDDLE  ALT=\"a%28x%5E2-4%29%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2%29%28x%2B2%29 ALIGN=MIDDLE  ALT=\"%28x-2%29%28x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-4 ALIGN=MIDDLE  ALT=\"x%5E2-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (use the difference of squares)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x%5E3-x%5E2-4x%2B4%29=0 ALIGN=MIDDLE  ALT=\"a%28x%5E3-x%5E2-4x%2B4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-4%29%28x-1%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-4%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E3-x%5E2-4x%2B4 ALIGN=MIDDLE  ALT=\"x%5E3-x%5E2-4x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the polynomial with roots of of <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;\" >, <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;\" >, or <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;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x%5E3-x%5E2-4x%2B4%29 ALIGN=MIDDLE  ALT=\"y=a%28x%5E3-x%5E2-4x%2B4%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=y=a%28x%5E3-x%5E2-4x%2B4%29 ALIGN=MIDDLE  ALT=\"y=a%28x%5E3-x%5E2-4x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24=a%280%5E3-0%5E2-4%280%29%2B4%29 ALIGN=MIDDLE  ALT=\"24=a%280%5E3-0%5E2-4%280%29%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=24 ALIGN=MIDDLE  ALT=\"y=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: a y-intercept of 24 means that the point (0,24) is on the graph which means that if <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;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=24 ALIGN=MIDDLE  ALT=\"y=24\"   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=24=a%284%29 ALIGN=MIDDLE  ALT=\"24=a%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F4=a ALIGN=MIDDLE  ALT=\"24%2F4=a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 4.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=a ALIGN=MIDDLE  ALT=\"6=a\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=6 ALIGN=MIDDLE  ALT=\"a=6\"   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=y=a%28x%5E3-x%5E2-4x%2B4%29 ALIGN=MIDDLE  ALT=\"y=a%28x%5E3-x%5E2-4x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to the previous equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6%28x%5E3-x%5E2-4x%2B4%29 ALIGN=MIDDLE  ALT=\"y=6%28x%5E3-x%5E2-4x%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=6 ALIGN=MIDDLE  ALT=\"a=6\"   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=y=6x%5E3-6x%5E2-6%284x%29%2B6%284%29 ALIGN=MIDDLE  ALT=\"y=6x%5E3-6x%5E2-6%284x%29%2B6%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6x%5E3-6x%5E2-24x%2B24 ALIGN=MIDDLE  ALT=\"y=6x%5E3-6x%5E2-24x%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=6x%5E3-6x%5E2-24x%2B24 ALIGN=MIDDLE  ALT=\"y=6x%5E3-6x%5E2-24x%2B24\"   DISABLED_style= \"max-width:90%; height:auto;\" > has the zeros <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;\" >, <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;\" >, or <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;\" > and has a y-intercept of 24. </SPAN>\n" );
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