Say there is the equation y=x squared for all x values 0 to 100 inclusive. A curve is made up of connecting the points, and so if there is an infinite amount of points in x from 0 to 100, the curve would be perfect.

However, say you can only have 8 points. One at x=0, the other at x=100. How do you select the other points such that it is as close to the original curve as possible? Thanks!