In many longitudinal clinical trial studies, quadratic growth curve mixed models are widely considered. Compared with the linear trend model, in some cases, adding a quadratic term to the time trend can give a better description of the relationship between the time measurement and response. Power analysis for the test on the treatment by time interaction has been studied in the linear trend mixed model. However, the existing research does not study this in the quadratic growth curve model. We conduct a power analysis for the test in the quadratic growth curve mixed model. A normal or chi-squared test is applied under the large sample case while an approximate t or F test is used in the small sample case. Power functions are presented for both large sample and small sample cases. We compare the theoretical power and the power given by a simulation study for these tests.