Electronic Proceedings of the Twentyeighth Annual International Conference on Technology in Collegiate MathematicsAtlanta, Georgia, March 1013, 2016Paper A040
This is an electronic reprint, reproduced by permission of Pearson Education Inc. Originally appeared in the Proceedings of the Twentyeighth Annual International Conference on Technology in Collegiate Mathematics, ISBN 013480029X, Copyright (C) 2017 by Pearson Education, Inc. 
Real Polynomials with a Complex Twist 
Michael Warren
Tarleton State University
mwarren@tarleton.edu
 John Gresham
Tarleton State University
jgresham@tarleton.edu
 Bryant Watt
Tarleton State University
wyatt@tarleton.edu

Click to access this paper:

Student appreciation of a function is enhanced by understanding the graphical
representation of that function. From the real graph of a polynomial, students can identify
realvalued solutions to polynomial equations that correspond to the symbolic
form. However, the real graph does not show the nonreal solutions to polynomial
equations. Instead of enhancing students’ idea of a function, the traditional graph implies
a clear disconnect from the symbolic form. In order to fully appreciate the Fundamental
Theorem of Algebra, and the nonreal solutions of a polynomial equation, traditional
graphs are inadequate. Since the early 20th century, mathematicians have tried to find a
way to augment the traditional Cartesian graph of a polynomial to show its complex
counterpart. Advancements in computer graphics allow us to easily illustrate a more
complete graph of polynomial functions that is still accessible to students of many different
levels. The authors will demonstrate a method using modern 3D graphical tools such as
GeoGebra to create dynamic visualizations of these more complete polynomial functions.
Keyword(s): GeoGebra