If a function p(x) has four distinct zeros, which of the following could represent the entire graph of p in a standard coordinate plane?

Options

A.
B.
C.
D.

Explanation

To solve the problem, we need to determine which graph represents a function \( p(x) \) that has four distinct zeros. A zero of a function is a value of \( x \) for which \( p(x) = 0 \), and graphically, these zeros correspond to the points where the graph intersects the x-axis.

### Step-by-Step Solution:

1. **Understand the Concept of Zeros**:
- Zeros of a function are the x-values where the function equals zero. In a graph, these are the points where the graph crosses the x-axis.

2. **Identify the Requirement**:
- We need to find a graph that intersects the x-axis at four distinct points. This means the graph must have four separate x-intercepts.

3. **Analyze the Options**:
- We will evaluate each option to see how many times it intersects the x-axis.

4. **Evaluate Option A**:
- Check how many times the graph intersects the x-axis.
- **Result**: It intersects the x-axis only two times.
- **Conclusion**: This option does not have four distinct zeros.

5. **Evaluate Option B**:
- Check how many times the graph intersects the x-axis.
- **Result**: It intersects the x-axis three times.
- **Conclusion**: This option does not have four distinct zeros.

6. **Evaluate Option C**:
- Check how many times the graph intersects the x-axis.
- **Result**: It intersects the x-axis two times.
- **Conclusion**: This option does not have four distinct zeros.

7. **Evaluate Option D**:
- Check how many times the graph intersects the x-axis.
- **Result**: It intersects the x-axis four times.
- **Conclusion**: This option has four distinct zeros.

8. **Final Decision**:
- Since only Option D intersects the x-axis four times, it is the correct representation of the function \( p(x) \) with four distinct zeros.

### Conclusion:
The correct answer is **Option D**.