Past research associated relative left frontal cortical activity with approach motivation, or the inclination to move toward a stimulus, as well as positive affect. Work with anger, a negative emotion often high in approach, helped clarify the role of relative left frontal cortical activity. Less work, however, examined positive emotional states varying in approach motivation and relative left frontal cortical activity. In the present research, it was predicted that positive facial expressions varying in degrees of approach motivation would influence relative left frontal cortical activity measured with electroencephalography (EEG) alpha power and task persistence measured with time working on insolvable geometric puzzles. Furthermore, relative left frontal cortical activity should positively relate to task persistence. In support of these predictions, determination compared to satisfaction facial expressions caused greater relative left frontal activity measured with EEG alpha power, a neural correlate of approach motivation. This effect remained when accounting for the contribution of muscle activity in the EEG signal, subjective task difficulty, and the extent to which participants made facial expressions. Determination compared to neutral facial expressions also caused greater self-reported interest following the puzzle task. Facial expressions did not directly influence task persistence. However, relative left frontal cortical activity was positively correlated with total time working on insolvable puzzles in the determination condition only. These results extend embodiment theories and motivational models of asymmetric frontal cortical activity.