The graph shows the path of the particle as the upper half of a circle with a center at $(2, -3)$ and a radius of 1. The particle starts at $(2, -2)$ (marked in green) and moves counterclockwise to $(2, -4)$ (marked in red).

Summary:

• Path: The upper half of the circle $(x - 2)^2 + (y + 3)^2 = 1$.
• Portion Traced: From $(2, -2)$ to $(2, -4)$.
• Direction of Motion: Counterclockwise.

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Related Questions:

1. How do we find parametric equations from a given Cartesian equation?
2. What are the parametric representations for standard geometric shapes like circles and ellipses?
3. How does changing the parameter interval affect the path traced by a particle?
4. What happens to the graph if the parameter interval is extended beyond $[0, \pi]$?
5. Can we express the path in polar coordinates instead of Cartesian?

Tip: When converting parametric equations to Cartesian form, always look for trigonometric identities or algebraic relationships to eliminate the parameter.