We demonstrate the simultaneous estimation of signal frequency and amplitude by a single quantum sensor in a single experimental shot. Sweeping the qubit splitting linearly across a span of frequencies induces a nonadiabatic Landau-Zener transition as the qubit crosses resonance. The signal frequency determines the time of the transition, and the amplitude its extent. Continuous weak measurement of this unitary evolution informs a parameter estimator retrieving precision measurements of frequency and amplitude. Implemented on radio-frequency-dressed ultracold atoms read out by a Faraday spin-light interface, we sense a magnetic signal with estimated sensitivities to amplitude of 11 pT/sqrt[Hz], frequency 0.026 Hz/Hz^{3/2}, and phase 0.084 rad/sqrt[Hz], in a single 300 ms sweep from 7 to 13 kHz. The protocol realizes a swept-sine quantum spectrum analyzer, potentially sensing hundreds or thousands of channels with a single quantum sensor.