The following tool will allow you to play around with Lagrange Polynomials. Enter a list of 7 values into the table below, or click on a button to import prefetched data.
x f(x)
1
2
3
4
5
6
7
The Lagrange Polynomial, below, passes through all the given data points.

Below is a table of values of the polynomial above, for various inputs, including inputs that correspond to past and future values!
Past Entered Values Future
-2 -1 0 1 2 3 4 5 6 7 8 9 10

Graph:

Questions to think about:
  1. The Lagrange Polynomial models the data you input exactly. Based on your observations, though, does it make sense to try to use Lagrange Polynomials to try to predict the future?
  2. To fit n data points, the Lagrange Polynomial is a polynomial of degree n-1. In the above case, n was 7. If you have 2 points, what would the Lagrange Polynomial look like?
Further reading/playing:
Zoomed out graph: