Investigating Families of Quartic Polynomials via a Computer Algebra System

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Alwis, T.d. (2001). Investigating Families of Quartic Polynomials via a Computer Algebra System. In J. Price et al. (Eds.), Proceedings of Society for Information Technology & Teacher Education International Conference 2001 (pp. 3176-3181). Chesapeake, VA: AACE.
Retrieved from http://www.editlib.org/p/17360.

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Conference Information

Society for Information Technology & Teacher Education International Conference (SITE) 2001
Norfolk, VA
2001
ISBN 1-880094-41-X
  Jerry Price, Dee Anna Willis, Niki Davis & Jerry Willis
AACE

More Information on SITE
Table of Contents

Author

Tilak de Alwis, Southeastern Louisiana University, United States

Abstract

Consider the one parameter family of quartic polynomials given by ) ( ) )( ( ) ( 2 b x t x a x x f - - - = where a and b are distinct real constants, and t is a real parameter. Let ) 0 , ( ), 0 , ( b B a A and ) 0 , (t C be its x-intercepts, and ) 2 , 0 ( abt D be its y-intercept. Suppose that the normal lines to the graph of f at the points A and B meet at R, and the tangent lines to the graph at those points meet at S. As the parameter t changes, the graph of f changes. However, the points A and B remain fixed while all other points C, D, R and S change. This paper discusses some geometric properties such as centroids, circumcenters, orthocenters, and locus problems of the variable triangles ABR, ABS etc.

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