https://file.aiquickdraw.com/mathbot/file/17268113960657nsuzu42.jpg

The problem asks for identifying certain features of the polynomial function based on its graph.

### Let's break it down:

1. **Degree of the polynomial (even or odd)**:
   - The graph shows symmetry, indicating the polynomial degree is **even**. Even-degree polynomials have ends that both point either up or down, and in this case, both ends point upwards.

2. **Leading coefficient**:
   - The leading coefficient affects the direction of the end behavior. Since both ends of the graph point upwards, the leading coefficient must be **positive**.

3. **Distinct real zeros**:
   - Distinct real zeros are where the graph crosses the x-axis. In this graph, it crosses the x-axis at three different points, so there are **3 distinct real zeros**.

4. **Relative extrema**:
   - Relative extrema refer to the local maxima and minima. The graph has two relative extrema: one local maximum and one local minimum. Hence, there are **2 relative extrema**.

### Answer Summary:
- The degree of \( f(x) \) is **even**.
- The leading coefficient is **positive**.
- There are **3 distinct real zeros**.
- There are **2 relative extrema**.

Would you like further details on any aspect of this problem? Here are five related questions for further practice:

1. What are the general characteristics of even-degree polynomials?
2. How does the leading coefficient influence the end behavior of a polynomial graph?
3. What distinguishes relative extrema from absolute extrema in polynomial functions?
4. How can you determine the exact zeros of a polynomial algebraically?
5. How would the graph change if the leading coefficient were negative?

**Tip:** Even-degree polynomials always have the same end behavior (either both ends up or both down) depending on the sign of the leading coefficient.

The polynomial function f(x) is graphed below. Fill in the form regarding the features of this graph.

Analyze the graph of a polynomial function by determining its degree, leading coefficient, distinct real zeros, and relative extrema. Suitable for high school students learning polynomial functions.

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