A study utilized the medical records of nursing home residents as the source of data for the study. ...

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Rationale 1: A longitudinal study follows subjects over time to determine effects of a phenomenon. There is not enough data in the question to determine if this is a longitudinal study.
Rationale 2: In a retrospective study, the dependent variable (effect) is identified in the present, and an attempt is made to determine the independent variable (cause) that occurred in the past.
Rationale 3: A prospective study identifies presence of an independent variable and follows subjects into the future to observe the dependent variable.
Rationale 4: A cross-sectional study examines subjects at a particular point in time.