Finding the best quadratic approximation of a function

Abstract

This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e^x . Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact that three non-collinear points determine a unique quadratic function. Three different techniques for measuring the error in the approximations are considered.

Keywords:

• quadratic approximation
• Taylor polynomial
• error in the approximation
• total error
• root-square error
• maximum error

Acknowledgements

The study described in this article was supported by the Division of Undergraduate Education of the National Science Foundation under grant nos. DUE-0089400 and DUE-0310123. However, the views expressed are not necessarily those of the Foundation.