By calculating the Finite differences, determine
a) which type of polynomial function best models this relationship.
x | y
-2 1
-1 0
0 1
1 16
2 81
3 256
4 625

Question

By calculating the Finite differences, determine
a) which type of polynomial function best models this relationship.
x         |        y
-2                1
-1                 0
0                  1
1                  16
2                  81
3                  256
4                 625

amistre64 · Answer

1          2         3        4       5
---------------------------
1           -1      +2   +12   +24
0          +1    +14   +36   +24
1        +15    +50   +60   +24
16      +65  +110   +84    ^^^^^^ it takes 5 times to get
81    +175  +194                      this to pan out the same;
256  +369                                this function could be a quartic ?
625

amistre64 · Answer

something akin to this:
$$x^5+x^4+x^3+x^2+x+c$$