2026-01-192026-01-192025-12-18https://repositorio.ifal.edu.br/handle/123456789/1377This work aims to study second-degree polynomial functions, emphasizing their historical aspects, graphs, and roots. The research initially addressed the historical context of mathematics, highlighting the contributions of Babylonian, Egyptian, Greek, and Indian civilizations to the development of quadratic equations. Subsequently, the main elements that compose a seconddegree function were analyzed, such as concavity, vertex, axis of symmetry, maximum and minimum points, as well as the sign of the function, emphasizing their graphical representations and applications. From this investigation, it was observed that the study of quadratic functions is fundamental to understanding the behavior of curves. Furthermore, its importance in the teaching-learning process was confirmed, as guided by the Brazilian National Common Curriculum Base (BNCC), by favoring logical reasoning, graphical interpretation, and problem-solving. Thus, this work demonstrates that the study of quadratic functions, when combined with their historical background and practical contextualization, contributes to a more meaningful and integrated learning of mathematics education.ptAttribution-NoDerivs 3.0 BrazilMatemáticaFunção quadráticaRepresentação gráficaHistória da matemáticaQuadratic functionHistory of mathematicsGraphical representationTrabalho de Conclusão de CursoCIENCIAS EXATAS E DA TERRA::MATEMATICA