here is a link to a desmos graph that allows you to adjust the a, b, c, and d values in these graphs. for y…

Explanation:

Step1: Recall amplitude formula

For $y = A\cos(Bx - C)+D$, the amplitude is $|A|$. In $y=-2\cos(x - \frac{\pi}{2})$, $A=-2$, so amplitude $= |-2| = 2$.

Step2: Recall period formula

The period of $y = A\cos(Bx - C)+D$ is $T=\frac{2\pi}{|B|}$. Here $B = 1$, so $T=\frac{2\pi}{|1|}=2\pi$.

Step3: Recall phase - shift formula

The phase - shift of $y = A\cos(Bx - C)+D$ is $\frac{C}{B}$. Here $C=\frac{\pi}{2}$ and $B = 1$, so phase - shift $=\frac{\frac{\pi}{2}}{1}=\frac{\pi}{2}$.

Answer:

Amplitude: 2 Period: $2\pi$ Phase - shift: $\frac{\pi}{2}$