Answer
See the full explanation below.
Work Step by Step
When the graph of $y=\sin 2x$ is shifted one unit upward, then the graph of $y=\sin 2x+1$ is obtained. For the standard function in the form $y=A\sin \left( Bx+C \right)$
$\begin{align}
& \text{Amplitude=}\left| A \right| \\
& \text{Period=}\frac{2\pi }{B} \\
& \text{Phase}\,\text{Shift}=\frac{C}{B}
\end{align}$
$\text{Quarter-period}=\frac{2\pi }{4}$
So, Amplitude is 0
The period is given below:
$\begin{align}
& \text{Period = }\frac{2\pi }{B} \\
& =\frac{2\pi }{2} \\
& =\pi
\end{align}$
Phase shift is 0
The quarter-period is as follows:
$\text{Quarter-period}=\frac{\pi }{4}$
Now, add quarter periods starting from $x=0$ to generate x-values for the key points. The x-value for the first key point is as follows:
$x=0$
] And the x-value for the second key point is:
$\begin{align}
& x=0+\frac{\pi }{4} \\
& =\frac{\pi }{4}
\end{align}$
And the x-value for the third key point is:
$\begin{align}
& x=\frac{\pi }{4}+\frac{\pi }{4} \\
& =\frac{\pi }{2}
\end{align}$
And the x-value for the fourth key point is:
$\begin{align}
& x=\frac{\pi }{2}+\frac{\pi }{4} \\
& =\frac{3\pi }{4}
\end{align}$
And the x-value for the fifth key point is:
$\begin{align}
& x=\frac{3\pi }{4}+\frac{\pi }{4} \\
& =\pi
\end{align}$
