1. **State the problem:** We need to determine the domain on which the given quadratic function is increasing. 2. **Identify the function type:** The graph is a downward-opening parabola with zeros near $x=-1$ and $x=8$, and a vertex at approximately $(3.5,8)$. 3. **Recall the properties of a parabola:** For a quadratic function $y = ax^2 + bx + c$ with $a < 0$, the parabola opens downward. It increases on the interval to the left of the vertex and decreases to the right. 4. **Find the vertex:** The vertex $x$-coordinate is given by $$x = -\frac{b}{2a}.$$ From the graph, the vertex is at $x \approx 3.5$. 5. **Determine the increasing interval:** Since the parabola opens downward, the function is increasing on $$(-1, 3.5)$$ approximately, starting from the left root near $-1$ up to the vertex at $3.5$. 6. **Final answer:** The function is increasing on the interval $$\boxed{(-1, 3.5)}.$$