a gate capacitor and by threading flux through a SQUID loop. We characterize this device and find excellent agreement between theory and experiment. A key difficulty in this characterization is the presence of frequency fluctuations comparable in scale to the cavity linewidth, which deform our measured resonance circles in accordance with recent theoretical predictions [B. L. Brock et al., Phys. Rev. Applied (to be published), arXiv:1906.11989]. By measuring the power spectral density of these frequency fluctuations at carefully chosen points in parameter space, we find that they are primarily a result of the 1/f charge and flux noise common in solid state devices. Notably, we also observe key signatures of frequency fluctuations induced by quantum fluctuations in the cavity field via the Kerr nonlinearity.