https://r2.erweima.ai/mathbot/image/17269578644749dqgiqff.jpg

### 1. **Type of Graph**:
   This is a **parabola**, which is the graph of a **quadratic function**.

### 2. **Degree of the Function**:
   The degree of the function is **2**, since it represents a quadratic equation. Quadratic functions have the form \( y = ax^2 + bx + c \), where the highest power of \( x \) is 2.

### 3. **Vertex**:
   The vertex of the parabola is the point \( (-3, -6) \). The vertex is a key point that defines the minimum (or maximum) of the quadratic function, and in this case, it's a **minimum** since the parabola opens upwards.

### 4. **Additional Information**:
   - The parabola opens **upward** because it curves upwards, indicating the coefficient of \( x^2 \) is positive.
   - The point \( (0, 3) \) represents the **y-intercept**, which is where the parabola crosses the y-axis.
   - The axis of symmetry is the vertical line \( x = -3 \), passing through the vertex.
   - Since the parabola opens upwards and the vertex is a minimum point, this graph models a function with a **minimum value** of \( -6 \) at \( x = -3 \).
   - The parabola appears symmetrical about the axis of symmetry.

Would you like more details or have any specific questions?

### Follow-up Questions:
1. How do we find the equation of the quadratic function from this graph?
2. What is the significance of the y-intercept in a quadratic function?
3. Can you explain how to determine whether a parabola opens upward or downward?
4. What does the vertex form of a quadratic equation tell us?
5. How can you find the x-intercepts (if any) of the parabola from the graph?

### Tip:
The **vertex form** of a quadratic function \( y = a(x - h)^2 + k \) makes it easy to identify the vertex, which is \( (h, k) \).

What type of graph is this? What is the degree of this function? What is the vertex? What else can you tell me about this graph?

This problem explores a quadratic function graph with a vertex at (-3, -6) and a y-intercept at (0, 3). Learn how to identify the graph type, degree of the function, vertex, and additional properties such as the axis of symmetry and minimum value. Suitable for Grades 8-10.

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