Finding polynomials from a set of coordinates

[SlideRule]

(03-10-2017 07:39 PM)tdh79 Wrote:  ... I need to find polynomial functions from a given set of coordinates, ...find the function and plot ...

A starting point is polynomial interpolation. Do you have a background in Technical Mathematics sufficient to identify the following;
a) Local Minima / Maxima
b) Inflection Points
on a data plot of cartesian coordinates?
Comprehension of these topics is not essential but will greatly facilitate the formulation of a solution for your proposition, such as the shape of the plot or the degree of the polynomial constituting the same plot.
"If you need the curve to pass through all the points in the data set, the only fool-proof way is to use a polynomial of degree (n-1) where n is the number of data points. If not, regression can be used." This process can be overwhelming while an inexact or approximate function may suffice within the required / implied accuracy /precision of the data set.
As in every problem, an initial estimate or approximation of the desired answer is welcome prior to a more rigorous and exacting analysis.
With a better understanding of your background, the application of the methods and procedures the many members have proffered may facilitate a most positive and productive learning experience for us all.

BEST!
SlideRule