MA(2) ACVF and ACF
Model
$$X_t = Z_t + \theta_1 Z_{t-1} + \theta_2 Z_{t-2}, \qquad Z_t \sim \text{WN}(0, \sigma^2)$$ACVF
$$\gamma(0) = (1 + \theta_1^2 + \theta_2^2)\sigma^2$$$$\gamma(1) = (\theta_1 + \theta_1\theta_2)\sigma^2$$$$\gamma(2) = \theta_2 \sigma^2$$$$\gamma(h) = 0, \quad |h| \geq 3$$ACF
$$\rho(h) = \begin{cases} 1, & h = 0 \\ \frac{\theta_1 + \theta_1\theta_2}{1 + \theta_1^2 + \theta_2^2}, & |h| = 1 \\ \frac{\theta_2}{1 + \theta_1^2 + \theta_2^2}, & |h| = 2 \\ 0, & |h| \geq 3 \end{cases}$$Summary
MA(2) is stationary. ACF cuts off after lag 2.