In the given graph, let's examine the zeros or x-intercepts to identify any multiplicity:

1. Zero at $D = (-2, 0)$:

   • The graph touches the x-axis and then rebounds. This suggests a zero with even multiplicity. Given the behavior of the graph at this point (a turning point where the graph doesn't cross the x-axis), it is likely to be a zero of multiplicity 2.

2. Zero at $E = (-1, 0)$:

   • The graph crosses the x-axis, indicating a zero with odd multiplicity. Since it appears to just cross the axis without any flattening or turning around, it likely has a multiplicity of 1.

3. Zero at $C = (2, 0)$:

   • Similar to point $E$, the graph crosses the x-axis, suggesting a zero with odd multiplicity. Again, it likely has a multiplicity of 1, as there is no indication of the graph flattening or turning around.

Summary of Multiplicities:

• $D = (-2, 0)$ has a multiplicity of 2.
• $E = (-1, 0)$ has a multiplicity of 1.
• $C = (2, 0)$ has a multiplicity of 1.

Explanation:

• A zero with even multiplicity (like $D = (-2, 0)$) will touch the x-axis and bounce back without crossing it. This is characteristic of a zero where the graph changes direction at the x-axis.
• A zero with odd multiplicity (like $E = (-1, 0)$ and $C = (2, 0)$) will cross the x-axis. This means the function changes sign at this point.

Would you like any further details or explanations?

Here are 5 questions you can ask next:

1. How does the multiplicity of a zero affect the shape of the graph at that point?
2. What are the implications of having a zero with even multiplicity in a polynomial function?
3. How can we determine the exact multiplicity of a zero algebraically?
4. What is the significance of the leading coefficient in determining the end behavior of a polynomial function?
5. How does the Fundamental Theorem of Algebra relate to the number of zeros of a polynomial function?

Tip: To confirm the multiplicity of a zero, look at the behavior of the graph near the zero and the corresponding factor in the polynomial equation.