Polynomial Fitting

[Desq]

Any help would be greatly appreciated!

 

[Steven G]

Your polynomial must contain the points (0,8), (1,9), (2,28), (3,83), (4, 192) and (5, 273).

Now you need to find a polynomial that contains these 6 points.

What should the degree of the polynomial be?

Post back showing your work?

 

[HallsofIvy]

Any set of n points can be given by a polynomial of degree n- 1. A polynomial of degree 5 can be fitted to 6 points.

Take f(x)= ax^5+ bx^4+ cx^3+ dx^2+ ex+ f and put in the 6 given points to get 6 equations to solve for a, b, c, d, e, and f.
f(0)= 8 so f= 8
f(1)= 9 so a+ b+ c+ d+ e+ f= 9
f(2)= 28 so 32a+ 16b+ 8c+ 4d+ 2e+ f= 28, etc.