Answer
The amplitude of the function is 2 and period is $4\pi $
Work Step by Step
The given equation is in the form of $y=A\cos Bx$.
Here, $A=-2\text{ and }B=\frac{1}{2}$
So, the amplitude is:
$\begin{align}
& \text{Amplitude=}\left| A \right| \\
& =\left| 2 \right| \\
& =2
\end{align}$
The period is:
$\begin{align}
& \text{Period = }\frac{2\pi }{B} \\
& =\frac{2\pi }{\left( \frac{1}{2} \right)} \\
& =4\pi
\end{align}$
$\text{Phase shift=}\frac{C}{B}=0$
The quarter period is as follows:
$\begin{align}
& \text{Quarter-period}=\frac{4\pi }{4} \\
& =\pi
\end{align}$
Now, add quarter periods starting from $x=\text{0}$ to generate x-values for the key points. The x-value for the first key point is as follows:
$x=\text{0}$
And the x-value for the second key point is:
$\begin{align}
& x=0+\pi \\
& =\pi
\end{align}$
And the x-value for the third key point is:
$\begin{align}
& x=\pi +\pi \\
& =2\pi
\end{align}$
And the x-value for the fourth key point is:
$\begin{align}
& x=2\pi +\pi \\
& =3\pi
\end{align}$
And the x-value for the fifth key point is:
$\begin{align}
& x=3\pi +\pi \\
& =4\pi
\end{align}$
