The one oldest problem that modern mathematicians and scientists often face is locating the correct/required solutions of polynomial equations called zeroes (roots). Quadratic polynomials that are the low order polynomials of degree 2 present mathematical expression where roots in general represent parabolic curves. With growing number of advancements and necessities in real time application, such as defining bounds of a set, nature of roots and their relationship in real space, etc. root-finding processes of current days mostly focus on three fundamental issues, that is, definition of space, location of roots and their approximation aspects. These concerns are being worked and have been substantially facilitated by well-established algebraic theorems. Most importantly, most works discuss an approximation and solution for a single root. Graphing is a tried and true method for approximating roots like this one. This study is inspired by the need to better understand the relationship between root connectivity and its application in the rapidly developing field of regional mapping. To ensure the continued viability of lower order polynomial applications, such as quadratic polynomials, this study correlates the limitations and scope that root finding techniques present during practical processes with the requirements of specificity, identifying the power, and distinctiveness that are used to overcome these obstacles. Newton's method of rational mapping based on root finding is detailed here to back up the article's claims. Based on previous work in this field, this study demonstrates the benefits of Newton-based rational mapping, highlighting its applicability to quadratic polynomials and its unique rigidity in dynamic settings.