https://r2.erweima.ai/mathbot/image/172483997735053py0ob1.jpg

The image you've uploaded shows a graph of a parabola, and it appears to be part of a math problem where you're asked to fill in a table with details about the graph.

### Here's how to analyze the graph:

1. **Number of Zeros**: 
   - Zeros are the points where the graph intersects the x-axis. This graph touches the x-axis at two points.

2. **Location of Zeros**: 
   - You would need to identify the x-coordinates where the graph crosses the x-axis. Based on the image, it seems the zeros are around \( x = -2 \) and \( x = 2 \).

3. **Y-intercept**: 
   - The y-intercept is where the graph crosses the y-axis. This point is where \( x = 0 \). In the graph, the y-intercept is at \( y = -4 \).

4. **Axis of Symmetry**:
   - The axis of symmetry is a vertical line that divides the parabola into two symmetrical halves. This line passes through the vertex. The x-coordinate of the vertex will be the equation for the axis of symmetry. In this case, the axis of symmetry appears to be \( x = 0 \).

5. **Maximum or Minimum Value**:
   - Since this is an upward-opening parabola, it has a minimum value at its vertex.

6. **Vertex**:
   - The vertex is the lowest point on the graph (since the parabola opens upwards). It appears to be at \( (0, -4) \).

### Summary to Fill in the Table:
- **Number of Zeros**: 2
- **Location of Zeros**: \( x = -2 \) and \( x = 2 \)
- **Y-intercept**: \( y = -4 \)
- **Axis of Symmetry**: \( x = 0 \)
- **Max/Min Value**: Minimum
- **Vertex**: \( (0, -4) \)

Would you like any further details or have any questions about this analysis?

### Follow-up Questions:
1. How do you determine if a parabola opens upwards or downwards?
2. What is the significance of the vertex in the context of a quadratic function?
3. Can you have a parabola with only one zero? Under what conditions?
4. How would the graph change if the quadratic function's leading coefficient is negative?
5. What does the axis of symmetry tell you about the properties of the parabola?

### Tip:
When analyzing the graph of a parabola, the vertex form of a quadratic equation \( y = a(x-h)^2 + k \) is particularly useful for quickly identifying the vertex \((h, k)\) and the direction of opening based on the sign of \(a\).

Explore the properties of a parabolic graph, including its zeros, vertex, y-intercept, axis of symmetry, and the direction of opening. Learn how to analyze and interpret the graph of a quadratic function with a detailed step-by-step solution.

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