This paper focuses on trajectory analysis that applies finite mixture modeling to longitudinal data. The paper introduces new modeling tools using semiparametric regression methods. A normal mixture is proposed such that the model contains one smooth term and a set of possible linear predictors. Model terms are estimated using a penalized likelihood method with the EM-algorithm. The paper also introduces a computationally appealing alternative that provides an approximate solution using ordinary linear model methodology developed for mixture regression and trajectory analysis. Simulation experiments and a real data example of height curves of 4,223 Finnish children illustrate the methods.