1. **State the problem:** Determine the domain on which the function represented by a downward-opening parabola with vertex at approximately $(-1,7)$ is increasing. 2. **Recall the properties of a parabola:** For a quadratic function $f(x) = ax^2 + bx + c$ with $a < 0$ (downward-opening), the vertex is the maximum point. 3. **Increasing and decreasing intervals:** The function is increasing on the interval to the left of the vertex and decreasing to the right of the vertex if $a < 0$. 4. **Identify the vertex:** Given vertex at $(-1,7)$, the function increases on $(-\infty, -1)$ and decreases on $(-1, \infty)$. 5. **Final answer:** The function is increasing on the domain $$(-\infty, -1)$$.