document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120017>Question 1120017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could someone please walk me through how to do this. It is a question from my test prep of advanced functions. \r<BR>\n" );
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document.write( "How do I determine the equation of the function that would model this data?\r<BR>\n" );
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document.write( "x 1,2,3,4,5,6<BR>\n" );
document.write( "f(x) 0,3,16,45,96,175\r<BR>\n" );
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document.write( "Any help would be so appreciated!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #735666 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=735666\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Six points uniquely determine a 5th-degree polynomial function.  (In general, n points uniquely determine an (n-1)th degree polynomial function).\r<BR>\n" );
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document.write( "The general form of a 5th-degree polynomial function is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ ax^5\ +\ bx^4\ +\ cx^3\ +\ dx^2\ +\ ex\ +\ f\">\r<BR>\n" );
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document.write( "So if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\ =\ 0\"> when <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 1\">, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ a\ +\ b\ +\ c\ +\ d\ +\ e\ +\ f\ =\ 0\">\r<BR>\n" );
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document.write( "And if <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\ =\ 3\"> when <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\ =\ 2\">, then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 32a\ +\ 16b\ +\ 8c\ +\ 4d\ +\ 2e\ +\ f\ =\ 3\">\r<BR>\n" );
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document.write( "Similarly:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 243a\ +\ 81b\ +\ 27c\ +\ 9d\ +\ 3e\ +\ f\ =\ 16\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1024a\ +\ 256b\ +\ 64c\ +\ 16d\ +\ 4e\ +\ f\ =\ 45\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 3125a\ +\ 625b\ +\ 125c\ +\ 25d\ +\ 5e\ +\ f\ =\ 96\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 7776a\ +\ 1296b\ +\ 216c\ +\ 36d\ +\ 6e\ +\ f\ =\ 175\">\r<BR>\n" );
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document.write( "Use Cramer's Rule to solve the 6X6 system.  Easiest is to put your matrices into Excel and use the MDETERM function to calculate the required determinants.\r<BR>\n" );
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document.write( "For example, your coefficient determinant and Da determinant will be:<BR>\n" );
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document.write( "     |    1    1    1    1    1   1|\r\n" );
document.write( "     |   32   16    8    4    2   1|\r\n" );
document.write( "D  = |  243   81   27    9    3   1|\r\n" );
document.write( "     | 1024  256   64   16    4   1|\r\n" );
document.write( "     | 3125  625  125   25    5   1|\r\n" );
document.write( "     | 7776 1296  216   36    6   1|\r\n" );
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document.write( "     |    0    1    1    1    1   1|\r\n" );
document.write( "     |    3   16    8    4    2   1|\r\n" );
document.write( "Da = |   16   81   27    9    3   1|\r\n" );
document.write( "     |   45  256   64   16    4   1|\r\n" );
document.write( "     |   96  625  125   25    5   1|\r\n" );
document.write( "     |  175 1296  216   36    6   1|\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "and so on...\r<BR>\n" );
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document.write( "You can also find an online matrix calculator that will do Gauss-Jordan reduction for you.  The only alternative to getting the exact answer by solving the 6X6 linear system is to use a \"curve of best fit\" calculator that will handle a 5th-degree polynomial model.  These generally result in inexact but very precise coefficients. <BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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