1. **State the problem:** We are given the function $y = -2 \cos(2x + 2\pi)$ and need to find its amplitude, period, and phase shift. 2. **Amplitude:** The amplitude of a cosine function $y = A \cos(Bx + C)$ is $|A|$. Here, $A = -2$, so the amplitude is: $$\text{Amplitude} = |-2| = 2$$ 3. **Period:** The period of a cosine function is given by: $$\text{Period} = \frac{2\pi}{|B|}$$ Here, $B = 2$, so the period is: $$\text{Period} = \frac{2\pi}{2} = \pi$$ 4. **Phase shift:** The phase shift is given by: $$\text{Phase shift} = -\frac{C}{B}$$ Here, $C = 2\pi$, so: $$\text{Phase shift} = -\frac{2\pi}{2} = -\pi$$ 5. **Summary:** - Amplitude: 2 - Period: $\pi$ - Phase shift: $-\pi$ These match the given graph description and values. **Final answer:** $$\text{Amplitude} = 2, \quad \text{Period} = \pi, \quad \text{Phase shift} = -\pi$$