https://file.aiquickdraw.com/mathbot/file/1730500838285psefc1uz.jpg

Let's analyze the graph to answer each part of the question:

### Observations:
This is a parabolic graph that opens downwards, suggesting that it represents a quadratic function with a negative leading coefficient.

### Answers:

1. **Sign of the Leading Coefficient (a):**  
   Since the parabola opens downward, the leading coefficient is **negative**.

2. **Vertex (b):**  
   The highest point on this graph (the vertex) is at **(-2, 4)**.

3. **Axis of Symmetry (c):**  
   The axis of symmetry for a parabola is a vertical line passing through the x-coordinate of the vertex. Here, it’s at **x = -2**.

4. **Intervals of Increase and Decrease (d):**  
   - **Increasing interval:** From **(-∞, -2)**, as the function values increase as x moves towards -2.
   - **Decreasing interval:** From **(-2, ∞)**, as the function values decrease as x moves away from -2.

5. **Domain and Range (e):**  
   - **Domain:** All real numbers, so **(-∞, ∞)**.
   - **Range:** Since the vertex is the maximum point at y = 4, the range is **(-∞, 4]**.

Would you like a further explanation for any part?

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Here are some additional related questions for practice:

1. What would be the effect on the graph if the leading coefficient were positive?
2. How would the axis of symmetry change if the vertex shifted?
3. Can you find the equation of this parabola based on the given vertex and symmetry?
4. What are the x-intercepts of this parabola, if any?
5. How would the intervals of increase and decrease change if the vertex were at a lower y-value?

**Tip:** The vertex form of a parabola is helpful in identifying the vertex and axis of symmetry quickly.

Use the graph to find the following: (a) Sign of the leading coefficient, (b) Vertex, (c) Axis of symmetry, (d) Intervals where f is increasing and where f is decreasing, (e) Domain and range

Learn how to analyze the graph of a parabola by identifying the vertex, axis of symmetry, sign of the leading coefficient, increasing and decreasing intervals, and the domain and range. This guide is ideal for students in Grades 9-10 studying quadratic functions and graphing techniques.

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