document.write( "Question 1119948: How do I determine the function that would model this data/ what should the final answer be?\r
\n" ); document.write( "\n" ); document.write( "x: 1, 2, 3, 4, 5, 6
\n" ); document.write( "f(x): 0, 3, 16, 45, 96, 175\r
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Algebra.Com's Answer #735599 by solver91311(24713)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); 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
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\n" ); document.write( "\n" ); document.write( "The general form of a 5th-degree polynomial function is:\r
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\n" ); document.write( "\n" ); document.write( "So if when , then\r
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\n" ); document.write( "\n" ); document.write( "And if when , then\r
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\n" ); document.write( "\n" ); 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
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\n" ); document.write( "\n" ); document.write( "For example, your coefficient determinant and Da determinant will be:
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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" );
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\n" ); document.write( "\n" ); document.write( "and so on...
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\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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