We'll find the interpolating polynomial passing through the points , , , using the Lagrange method.
We first use the formula to write the following:
After some simplification, we get:
And our answer:
Now we'll add a point to our data set, and find a new interpolating polynomial. Let us add the point to our set. Starting over with the Lagrange formula, we write:
Simplifying, we get:
And our polynomial is: