Answer
The amplitude is $\frac{1}{4}$, the period is $3\pi$, the vertical translation is $3$ units up and there is no phase shift.
Work Step by Step
We first write the equation in the form $y=c+a \cos [b(x-d)]$. Therefore, $y=3-\frac{1}{4}\cos (\frac{2}{3}x)$ becomes $y=3-\frac{1}{4}\cos [\frac{2}{3}(x-0)]$
Comparing the two equations, $a=-\frac{1}{4},b=\frac{2}{3},c=3$ and $d=0$.
The amplitude is $|a|=|-\frac{1}{4}|=\frac{1}{4}.$
The period is $\frac{2\pi}{b}=\frac{2\pi}{2/3}=3\pi$.
The vertical translation is $c=3$.
The phase shift is $|d|=|0|=0$
Therefore, the amplitude is $\frac{1}{4}$, the period is $3\pi$, the vertical translation is $3$ units up and there is no phase shift.
