Answer
The amplitude of the function is $\frac{5}{2}$, period is $\pi $, and phase shift is $-\frac{\pi }{4}$
Work Step by Step
Rewrite the given equation as $y=\frac{5}{2}\sin \left( 2x-\left( -\frac{\pi }{2} \right) \right)$.
Now, the provided equation is in the form of $y=A\sin \left( Bx-C \right)$.
Here, $A=\frac{5}{2},\text{ }B=2\text{ and }C=-\frac{\pi }{2}$
So, the amplitude is:
$\begin{align}
& \text{Amplitude=}\left| A \right| \\
& =\left| \frac{5}{2} \right| \\
& =\frac{5}{2}
\end{align}$
The period is given below:
$\begin{align}
& \text{Period = }\frac{2\pi }{B} \\
& =\frac{2\pi }{2} \\
& =\pi
\end{align}$
The phase shift is:
$\begin{align}
& \text{Phase shift = }\frac{C}{B} \\
& =\frac{\left( \frac{-\pi }{2} \right)}{2} \\
& =-\frac{\pi }{4}
\end{align}$
And the quarter period is as follows:
$\text{Quarter-period}=\frac{\pi }{4}$
Now, add quarter periods starting from $x=-\frac{\pi }{4}$ to generate x-values for the key points. The x-value for the first key point is as follows:
$x=-\frac{\pi }{4}$
And the x-value for the second key point is:
$\begin{align}
& x=-\frac{\pi }{4}+\frac{\pi }{4} \\
& =0
\end{align}$
And the x-value for the third key point is:
$\begin{align}
& x=0+\frac{\pi }{4} \\
& =\frac{\pi }{4}
\end{align}$
And the x-value for the fourth key point is:
$\begin{align}
& x=\frac{\pi }{4}+\frac{\pi }{4} \\
& =\frac{\pi }{2}
\end{align}$
And the x-value for the fifth key point is:
$\begin{align}
& x=\frac{\pi }{2}+\frac{\pi }{4} \\
& =\frac{3\pi }{4}
\end{align}$
