The graph in the image is of a cosine function that is vertically flipped and shifted. Let's break down the information provided by the graph and construct the equation in the form $y = A \cos(\omega x)$.

1. Amplitude (A): The graph reaches a maximum of 10 and a minimum of -10, which means the amplitude is 10. The negative sign indicates that the graph is reflected vertically, so $A = -10$.

2. Period (T): The period is the horizontal distance required for the graph to complete one full cycle. From the graph, it completes one full cycle from $x = -2\pi$ to $x = 6\pi$. Thus, the period is $6\pi - (-2\pi) = 8\pi$.

   The period $T$ of a cosine function is related to $\omega$ by the formula: $T = \frac{2\pi}{\omega}$ Setting $T = 8\pi$, we get: $8\pi = \frac{2\pi}{\omega}$ Solving for $\omega$: $\omega = \frac{2\pi}{8\pi} = \frac{1}{4}$

3. Equation: Now, using these values, the equation of the cosine function is: $y = -10 \cos\left(\frac{1}{4}x\right)$

Thus, the equation for the graph is: $y = -10 \cos\left(\frac{1}{4}x\right)$

Would you like more details or have any questions about this? Here are 5 related questions to expand your understanding:

1. How does the amplitude affect the graph of a trigonometric function?
2. What does it mean when a cosine function is reflected vertically?
3. How can you determine the phase shift of a cosine or sine function?
4. What are the differences between sine and cosine functions in terms of their graphs?
5. How do changes in $\omega$ affect the frequency of a cosine or sine function?

Tip: The phase shift of a trigonometric function occurs when the graph is shifted horizontally. Keep an eye on this when analyzing equations like $A \sin(\omega x + \phi)$.