Exploring high school students’ understanding and difficulties in connecting discriminant of quadratic equations and graphs of quadratic functions

This study investigates how high school students understand and connect the discriminant of quadratic equations with the graph of quadratic functions, and explores the cognitive, contextual, and affective difficulties they experience in the process.A task-based survey was administered to 87 Grade 11 students who had completed the corresponding curriculum contents, followed by in-depth interviews with selected participants based on their survey responses.The survey questions were designed to assess the level of understanding in connecting algebraic and graphical representations of functions, while the interview probed their cognitive, contextual, and affective aspects in graph interpretation.The results indicate that students tended to favor problem-solving strategies relying on the discriminant as an algebraic tool, while demonstrating limited engagement in drawing or interpreting graphs for problem-solving.This tendency appears to be linked to fragmentary conceptual understanding of graphs, difficulties in selecting appropriate strategies for given contexts, and affective factors such as anxiety or avoidance related to graph use.The study highlights the need for instructional strategies that support students emotionally and promote meaningful connections between mathematical representations, enabling them to apply such connections effectively in problem-solving.