Answer
The amplitude is $2$, the period is $8\pi$, the vertical translation is $1$ unit up and there is no phase shift.
Work Step by Step
We first write the equation in the form $y=c+a \sin [b(x-d)]$. Therefore, $y=1+2\sin\frac{1}{4}x$ becomes $y=1+2\sin[\frac{1}{4}(x-0)]$
Comparing the two equations, $a=2,b=\frac{1}{4},c=1$ and $d=0$.
The amplitude is $|a|=|2|=2.$
The period is $\frac{2\pi}{b}=\frac{2\pi}{0.25}=8\pi$.
The vertical translation is $c=1$.
The phase shift is $|d|=|0|=0$
Therefore, the amplitude is $2$, the period is $8\pi$, the vertical translation is $1$ unit up and there is no phase shift.
