https://r2.erweima.ai/mathbot/image/1726280918751z5j7h8u9.jpg

The graph shown in the image is a parabola, which opens upwards. Let's analyze the key points based on the graph:

### 1. **Vertex**:
The vertex of the parabola is the point where the curve reaches its minimum value (since it opens upward). Based on the graph, the vertex appears to be at the point **(0, -5)**.

### 2. **Line of Symmetry**:
The line of symmetry is a vertical line that passes through the vertex of the parabola. For this graph, since the vertex is at (0, -5), the line of symmetry is the vertical line **x = 0**.

### 3. **Nature of the Vertex**:
Since the parabola opens upwards and the vertex represents the minimum point on the graph, the vertex is a **minimum**.

### Final Answers:
- The vertex is **(0, -5)**, and it is a **minimum**.
- The line of symmetry is **x = 0**.

Would you like more details or clarifications? Here are five related questions to deepen your understanding:

1. What is the equation of the parabola based on its vertex and general shape?
2. How do you find the equation of the axis of symmetry for any parabola?
3. What is the standard form of a quadratic equation, and how can you use it to determine the vertex?
4. What would the graph look like if the parabola opened downwards?
5. How do the coefficients in a quadratic equation affect the width and direction of the parabola?

**Tip**: The line of symmetry of a parabola always passes through the vertex and is vertical, following the equation \( x = h \), where \( h \) is the x-coordinate of the vertex.

Answer the following questions about the graph: The vertex is [blank], and is a [blank]. The line of symmetry is [blank].

Learn how to identify the vertex and line of symmetry of a parabola. This problem covers key algebraic concepts related to parabolas, suitable for Grades 9-10.

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