SOLUTION: How do I determine the function that would model this data/ what should the final answer be? x: 1, 2, 3, 4, 5, 6 f(x): 0, 3, 16, 45, 96, 175 Any help would be so appreciated

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do I determine the function that would model this data/ what should the final answer be? x: 1, 2, 3, 4, 5, 6 f(x): 0, 3, 16, 45, 96, 175 Any help would be so appreciated      Log On


   

Question 1119948: How do I determine the function that would model this data/ what should the final answer be?
x: 1, 2, 3, 4, 5, 6
f(x): 0, 3, 16, 45, 96, 175
Any help would be so appreciated! Thank you!
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Six points uniquely determine a 5th-degree polynomial function. (In general, n points uniquely determine an (n-1)th degree polynomial function).

The general form of a 5th-degree polynomial function is:



So if when , then



And if when , then



Similarly:









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.

For example, your coefficient determinant and Da determinant will be:
     |    1    1    1    1    1   1|
     |   32   16    8    4    2   1|
D  = |  243   81   27    9    3   1|
     | 1024  256   64   16    4   1|
     | 3125  625  125   25    5   1|
     | 7776 1296  216   36    6   1|

     |    0    1    1    1    1   1|
     |    3   16    8    4    2   1|
Da = |   16   81   27    9    3   1|
     |   45  256   64   16    4   1|
     |   96  625  125   25    5   1|
     |  175 1296  216   36    6   1|


and so on...


John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
Even more easy way is to use an online free of charge solver for systems of linear equations, for, example, this one

http://matrix.reshish.com/gauss-jordanElimination.php