https://file.aiquickdraw.com/mathbot/file/17285324345966lq66m9u.jpg

Let's analyze the graph.

This is a degree 6 polynomial with three distinct roots. Based on the graph:

- **Root 1**: The zero at \(x = -1\). Since the graph only touches the x-axis at this point and turns around, the **multiplicity** is **2**. This indicates a double root.
- **Root 2**: The zero around \(x = 0.5\). The graph crosses the x-axis at this point, indicating a **multiplicity of 1**.
- **Root 3**: The zero around \(x = 2\). The graph also crosses the x-axis here, which means the **multiplicity is 1**.

### Answer summary:
- Root 1: Zero at \(x = -1\), Multiplicity = 2
- Root 2: Zero at \(x = 0.5\), Multiplicity = 1
- Root 3: Zero at \(x = 2\), Multiplicity = 1

Let me know if you'd like more details or clarifications!

Here are five related questions for practice:
1. What does the multiplicity of a root signify in the graph of a polynomial?
2. How does the degree of a polynomial affect the number of roots it can have?
3. What happens to the behavior of the graph near roots with even multiplicity versus odd multiplicity?
4. How do you determine the total number of turning points in a polynomial based on its degree?
5. If a polynomial has a root with multiplicity 3, how does it behave near that root?

**Tip**: For polynomial graphs, roots with even multiplicities "bounce" off the x-axis, while those with odd multiplicities pass through it.

The graph of a degree 6 polynomial has three distinct roots. Identify the roots and their multiplicities.

This problem involves identifying the roots and multiplicities of a degree 6 polynomial. The graph shows three distinct roots at x = -1 (multiplicity 2), x = 0.5 (multiplicity 1), and x = 2 (multiplicity 1). Explore the behavior of polynomials near roots with different multiplicities.

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