Answer
The equation of the graph is $\underline{y=2\cos \left( \frac{\pi x}{4} \right)}.$
Work Step by Step
The graph is of the form $y=A\cos Bx,$
$\begin{align}
& A=\text{Amplitude of the graph}\text{.} \\
& B=\text{ }\frac{2\pi }{\text{period}} \\
\end{align}$
Amplitude $A$ is the maximum value of the graph $y.$
In the provided graph shown above, the maximum value of $y$ means the amplitude is 2. So:
$A=2$
The time period means the magnitude measured, along the $x$ axis, between two adjacent equal magnitude values of y. Here the time period is 8 as shown above.
Therefore,
$\begin{align}
& B=\text{ }\frac{2\pi }{\text{period}} \\
& =\frac{2\pi }{8} \\
& =\frac{\pi }{4}
\end{align}$
Putting the values of $A\text{ and }B$ in the general form of the graph $y=A\cos Bx,$ we get:
$y=2\cos \left( \frac{\pi x}{4} \right)$
