We develop an understanding of the relationship between the symmetry of polynomial graphs and the calculus that underlies this symmetry. We arrive at a method to determine whether a single-variable polynomial with real coefficients has a symmetric graph. We then encode this method into a closed formula that is a necessary and sufficient condition for the polynomial to have symmetry.

Author Bio

Peter Cermak is a current undergraduate at Christendom College. He is a mathematics major who will graduate in May of 2021. His areas of interest include geometry and number theory, which he plans to study in graduate school. A Christendom College President's Scholar, and a member of the Honors Program, Mr. Cermak strives for academic excellence in all areas of study.