A theoretical-didactic proposal based on variational ideas and the use of GeoGebra is described as a response to a local problem on the understanding of the concept of function and quadratic equation in pre-university students. The theoretical elements of this work are based on the understanding of concepts and the theory of semiotic registers and representations, while the methodological references were based on hypothetical learning trajectories and the use of dynamic software, considered as a heuristic resource. The proposal was validated by means of expert criteria. This elaboration contributes with a proposal that breaks with the classical schemes of presentation and treatment of the content, which favors through the incorporation of variational ideas generated with the dynamic software GeoGebra the understanding of the articulated concepts of function and quadratic equation in pre-university students.