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Let's analyze the given problem step by step:

### Graph Characteristics:
The equation is of the form:

\[
y = A \cos(\omega x) + B
\]

where:
- \( A < 0 \) (amplitude),
- \( B > 0 \) (vertical shift), and
- \( 0 < \omega < 2\pi \) (angular frequency).

The graph has a maximum value of 3 and a minimum value of -3, which gives the following information:
- The **vertical shift** \( B \) is the average of the maximum and minimum values, calculated as:

\[
B = \frac{3 + (-3)}{2} = 0
\]

Thus, \( B = 0 \), and there is no vertical shift. The graph oscillates around the x-axis.

The **amplitude** \( A \) is the distance from the midline (in this case, the x-axis) to the maximum or minimum values, which gives \( |A| = 3 \). Since \( A < 0 \), we conclude \( A = -3 \).

### Period:
To determine \( \omega \), we need the period of the function. The period is the length of one complete cycle, which is from \( -\frac{7}{8} \) to \( \frac{7}{4} \).

- The period is the difference between these two values:

\[
\text{Period} = \frac{7}{4} - \left(-\frac{7}{8}\right) = \frac{7}{4} + \frac{7}{8}
\]

To add these, let's find a common denominator:

\[
\frac{7}{4} + \frac{7}{8} = \frac{14}{8} + \frac{7}{8} = \frac{21}{8}
\]

Thus, the period of the cosine function is \( \frac{21}{8} \).

The period of a cosine function is given by \( \frac{2\pi}{\omega} \), so we can solve for \( \omega \):

\[
\frac{2\pi}{\omega} = \frac{21}{8}
\]

Solving for \( \omega \), we get:

\[
\omega = \frac{2\pi \cdot 8}{21} = \frac{16\pi}{21}
\]

### Final Equation:
The equation of the graph is:

\[
y = -3 \cos\left(\frac{16\pi}{21}x\right)
\]

Would you like more details or explanations? Here are some related questions:

1. How do you calculate the amplitude from a graph?
2. What does the period of a cosine function represent?
3. How can you determine the vertical shift of a trigonometric function?
4. What is the general form of the cosine function, and how do different parameters affect it?
5. How do you solve for \( \omega \) using the period of a cosine function?

**Tip**: When solving trigonometric equations, carefully observe the amplitude, period, and vertical shift to correctly determine each parameter.

Find an equation for the graph shown. Type the equation of the given graph in the form y = A cos(ωx) + B, in which A < 0, B > 0 and 0 < ω < 2π. The graph has specific points that determine the amplitude, period, and frequency.

Learn how to find the equation of a cosine graph based on its amplitude, period, and frequency. This problem demonstrates the key concepts of trigonometric functions, perfect for high school students exploring cosine transformations.

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