document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102896>Question 1102896</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you find the polynomial whose graph goes through these points? \r<BR>\n" );
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document.write( "(2,10), (-1,-4), (0,2), and (1,-2).\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717613 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=717613\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You can use EXCEL to do a curve fit.<BR>\n" );
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document.write( "You can use linear algebra to solve a system of equations using a general form of the polynomial.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=Ax%5E3%2BBx%5E2%2BCx%2BD ALIGN=MIDDLE  ALT=\"y=Ax%5E3%2BBx%5E2%2BCx%2BD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "(2,10):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=A%282%29%5E3%2BB%282%29%5E2%2BC%282%29%2BD ALIGN=MIDDLE  ALT=\"10=A%282%29%5E3%2BB%282%29%5E2%2BC%282%29%2BD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8A%2B4B%2B2C%2BD=10 ALIGN=MIDDLE  ALT=\"8A%2B4B%2B2C%2BD=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(-1,-4):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=A%28-1%29%5E3%2BB%28-1%29%5E2%2BC%28-1%29%2BD ALIGN=MIDDLE  ALT=\"-4=A%28-1%29%5E3%2BB%28-1%29%5E2%2BC%28-1%29%2BD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-A%2BB-C%2BD=-4 ALIGN=MIDDLE  ALT=\"-A%2BB-C%2BD=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(0,2):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=A%280%29%5E3%2BB%280%29%5E2%2BC%280%29%2BD ALIGN=MIDDLE  ALT=\"2=A%280%29%5E3%2BB%280%29%5E2%2BC%280%29%2BD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=2 ALIGN=MIDDLE  ALT=\"D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1,-2):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2=A%281%29%5E3%2BB%281%29%5E2%2BC%281%29%2BD ALIGN=MIDDLE  ALT=\"-2=A%281%29%5E3%2BB%281%29%5E2%2BC%281%29%2BD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BB%2BC%2BD=-2 ALIGN=MIDDLE  ALT=\"A%2BB%2BC%2BD=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then substitute eq. 3 into the others,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8A%2B4B%2B2C%2B2=10 ALIGN=MIDDLE  ALT=\"8A%2B4B%2B2C%2B2=10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8A%2B4B%2B2C=8 ALIGN=MIDDLE  ALT=\"8A%2B4B%2B2C=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4A%2B2B%2BC=4 ALIGN=MIDDLE  ALT=\"4A%2B2B%2BC=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-A%2BB-C%2B2=-4 ALIGN=MIDDLE  ALT=\"-A%2BB-C%2B2=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "6.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-A%2BB-C=-6 ALIGN=MIDDLE  ALT=\"-A%2BB-C=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BB%2BC%2B2=-2 ALIGN=MIDDLE  ALT=\"A%2BB%2BC%2B2=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "7.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BB%2BC=-4 ALIGN=MIDDLE  ALT=\"A%2BB%2BC=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Continuing, add eq. 5 and eq. 7 to eq. 6 to eliminate C.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4A%2B2B%2BC-A%2BB-C=4-6 ALIGN=MIDDLE  ALT=\"4A%2B2B%2BC-A%2BB-C=4-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "8.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3A%2B3B=-2 ALIGN=MIDDLE  ALT=\"3A%2B3B=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BB%2BC-A%2BB-C=-4-6 ALIGN=MIDDLE  ALT=\"A%2BB%2BC-A%2BB-C=-4-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2B=-10 ALIGN=MIDDLE  ALT=\"2B=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "9.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-5 ALIGN=MIDDLE  ALT=\"B=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then working backwards,<BR>\n" );
document.write( "from eq. 8,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3A%2B3%28-5%29=-2 ALIGN=MIDDLE  ALT=\"3A%2B3%28-5%29=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3A=-2%2B15 ALIGN=MIDDLE  ALT=\"3A=-2%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=13%2F3 ALIGN=MIDDLE  ALT=\"A=13%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and from eq. 7,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F3-5%2BC=-4 ALIGN=MIDDLE  ALT=\"13%2F3-5%2BC=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F3-15%2F3%2BC=-12%2F3 ALIGN=MIDDLE  ALT=\"13%2F3-15%2F3%2BC=-12%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-12%2F3%2B2%2F3 ALIGN=MIDDLE  ALT=\"C=-12%2F3%2B2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=-10%2F3 ALIGN=MIDDLE  ALT=\"C=-10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%2813%2F3%29x%5E3-5x%5E2-%2810%2F3%29x%2B2 ALIGN=MIDDLE  ALT=\"y=%2813%2F3%29x%5E3-5x%5E2-%2810%2F3%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Of course, it matches the EXCEL curve fit.<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );