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 $x = -\frac{b}{2a}$.