https://file.aiquickdraw.com/mathbot/file/1730500705069d1zhgnhs.jpg

Based on the graph in the image, here are the answers to each part:

**(a) Sign of the leading coefficient:**  
The parabola opens upwards, indicating that the leading coefficient is **positive**.

**(b) Vertex:**  
The lowest point on the graph is the vertex, located at **(-2, -1)**.

**(c) Axis of symmetry:**  
The axis of symmetry is a vertical line passing through the x-coordinate of the vertex. Thus, the equation is:
\[
x = -2
\]

**(d) Intervals where \( f \) is increasing and where \( f \) is decreasing:**  
- **Decreasing interval:** From \( x = -\infty \) to \( x = -2 \).
- **Increasing interval:** From \( x = -2 \) to \( x = +\infty \).

**(e) Domain and range:**  
- **Domain:** The parabola extends indefinitely in both directions along the x-axis, so the domain is all real numbers:
  \[
  (-\infty, \infty)
  \]
- **Range:** The minimum value of \( f(x) \) is at \( y = -1 \), and it extends to positive infinity, so the range is:
  \[
  [-1, \infty)
  \]

Would you like further details or have any questions?

### Additional Questions
1. How do you determine the direction a parabola opens?
2. What effect does the leading coefficient have on the width of a parabola?
3. How is the vertex form of a quadratic equation derived?
4. Why does the range of this function start from \(-1\)?
5. How can the axis of symmetry help in graphing parabolas?

**Tip:** The axis of symmetry for a quadratic function \( f(x) = ax^2 + bx + c \) is always located at \( x = -\frac{b}{2a} \).

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 a quadratic graph to find the leading coefficient sign, vertex, axis of symmetry, intervals of increase and decrease, and domain and range. This problem covers key algebraic concepts, including the properties of parabolas, and is suitable for high school students.

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