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
And if
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
