The electric potential is often represented graphically using equipotential lines. Representing a multivariable function like the electric potential in this way can be challenging to interpret, and it is often helpful to make sense of a contour graph by making connections to other physical and mathematical ideas. We describe how upperlevel physics students make sense of two-dimensional equipotential graphs representing the electric potential. Our data are the students' responses to a matched pair of open-ended questions given at the beginning and end of a junior-level electrostatics course. Students predominantly discussed the sign, shape, and location of the charged objects that give rise to the potential. We also find that, while some students discuss how the potential changes in space, they rarely connect the potential explicitly to an electric field, even after junior-level instruction on electrostatics.