Finding polynomials from a set of coordinates

[grsbanks]

(03-10-2017 07:39 PM)tdh79 Wrote:  I need to find polynomial functions from a given set of coordinates, does anyone know how to do this with the 50g?

Fitting a polynomial to a set of coordinates can be done by changing your system into a set of linear equations that you then resolve using the Gauss-Jourdain pivot method.

One thing you need to know is that you need n+1 points to fit a polynomial of degree n. Eg. you need 2 points to fit a line (a.x + b = 0), 3 points to fit a quadratic (a.x² + b.x + c = 0) etc.

Eg. You have the points (-3,1), (1,0) and (2,1).

For the quadratic to fit, all of these points must satisfy the equation, so substituting the coordinates' values of x and y in the equation you end up with something like this:

a.(-3)² + b.(-3) + c = 1
a.1² + b.1 + c = 0
a.2² + b.2 +c = 1

-- or --

9a -3b +c = 1
a + b + c = 0
4a + 2b + c = 1

That looks suspiciously like a system of 3 linear equations that you can solve directly on the HP 50g. You will then get your values of a, b and c that you can replace in your quadratic equation and hey presto, there's your polynomial that passes through your three points.

The solution to this system is a=1/4, b=1/4 and c=-1/2

If you plot f(x)=(x^2)/4 + x/4 - 1/2 you'll see that the curve passes through all three points.