This paper presents a machine-learning-based joint model of brain age and cognitive performance, and demonstrates its superior performance relative to isolated models. Previous studies have chosen to study those two measures of brain health separately for two reasons: 1) although cognition can be measured regardless of an individual's health, brain-age ground-truth can be defined only for healthy individuals; and 2) while brain-age models are developed using neuroimaging data alone, modeling of cognitive performance additionally requires measures of cognitive reserve and biomarkers of cognitive disorders. However, those two measures are biologically related to each other, because they both depend on brain structure. Hence, we developed a joint model by 1) explicitly defining the commonalities and differences between them in a graph, and 2) converting that graph into a multitask-learning model to facilitate learning from population-level data. Our model took as inputs structural neuroimaging data and information related to cognitive reserve and disorders, and predicted brain age and cognitive performance in terms of a Mini-Mental State Examination (MMSE) score. We implemented linear and nonlinear joint models and compared them against isolated models. Our results indicate that joint modeling substantially improves the accuracy of the modeling of individual measures, relative to isolated models.