Solution

The energy (and hence the square of the amplitude of the velocity) of a weakly-damped forced oscillator, where $\gamma\ll\omega_0$, near resonance is proportional to

$$\frac{1}{(\omega-\omega_0)^2+\gamma^2}.$$

This means that the resonance curve peaks at $\omega=\omega_0$ and the width of the curve at half of the maximum height is $2\gamma$. Reading from the provided graph, we have $\omega_0\approx540$ s$^{-1}$ and $\gamma\approx60$ s$^{-1}$, and the quality factor is $Q=\omega_0/(2\gamma)\approx4.5$.