Time-lapse imaging is a powerful approach to gain insight into the dynamic responses of cells, but the quantitative analysis of morphological changes over time is a challenge. Here, we exploit the concept of "trajectory embedding" to analyze cellular behavior using morphological feature trajectory histories, i.e., multiple time points simultaneously, rather than the more common practice of examining morphological feature time courses in single timepoint (snapshot) morphological features. We apply this approach to analyze live-cell images of MCF10A mammary epithelial cells after treatment with a panel of microenvironmental perturbagens that strongly modulate cell motility, morphology, and cell cycle behavior. Our morphodynamical trajectory embedding analysis constructs a shared cell state landscape revealing ligand-specific regulation of cell state transitions and enabling quantitative and descriptive models of single-cell trajectories. Additionally, we show that incorporation of trajectories into single-cell morphological analysis enables (i) systematic characterization of cell state trajectories, (ii) better separation of phenotypes, and (iii) more descriptive models of ligand-induced differences as compared to snapshot-based analysis. This morphodynamical trajectory embedding is broadly applicable for the quantitative analysis of cell responses via live-cell imaging across many biological and biomedical applications.