**ERIC Number:**EJ1044514

**Record Type:**Journal

**Publication Date:**2014-Sep

**Pages:**10

**Abstractor:**ERIC

**Reference Count:**3

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

Interpolation and Polynomial Curve Fitting

Yang, Yajun; Gordon, Sheldon P.

Mathematics Teacher, v108 n2 p132-141 Sep 2014

Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lower-degree polynomial curve determine a cubic function. In general, n + 1 points uniquely determine a polynomial of degree n, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a polynomial is called interpolation, and the two most important approaches used are Newton's and Lagrange's interpolating formulas. Each has its advantages and disadvantages, which will be discussed in this article. The authors show how both approaches can be introduced and developed at the precalculus level in the context of fitting polynomials to data. These methods bring some of the most powerful and useful tools of numerical analysis to the attention of students who are still at the introductory level while building on and reinforcing many fundamental ideas in algebra and precalculus mathematics.

Descriptors: Mathematical Formulas, Calculus, Algebra, Mathematical Concepts, Equations (Mathematics), Introductory Courses

National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/

**Publication Type:**Journal Articles; Guides - Classroom - Teacher; Reports - Descriptive

**Education Level:**N/A

**Audience:**Teachers

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A