To find the point that is symmetrical to \((-1, -17)\) with respect to the graph of the equation \(y = -x^2 - 16\), we first need to find the vertex of the parabola defined by the equation.
The general form of the given equation, \(y = -x^2 - 16\), indicates that it is a downward-opening parabola. To find the vertex, we notice that the equation can be rewritten in vertex form. Here it is clear that the vertex occurs where \(x = 0\):
\[ y = -0^2 - 16 = -16 \]
So, the vertex of the parabola is at the point \((0, -16)\).
Next, we need to find the line of symmetry for the parabola, which is vertical and passes through the vertex. Since the vertex is at \(x = 0\), the line of symmetry is \(x = 0\).
To find the symmetrical point, we need to reflect the point \((-1, -17)\) across the line \(x = 0\). The reflection across this line can be found by changing the sign of the x-coordinate:
- The x-coordinate of \((-1, -17)\) is \(-1\). Its reflection across the line \(x=0\) will be \(1\).
- The y-coordinate remains the same, so it will be \((-17)\).
Thus, the symmetrical point is \((1, -17)\).
In conclusion, the point that is symmetrical to \((-1, -17)\) with respect to the graph of \(y = -x^2 - 16\) is
\[ \boxed{(1, -17)}. \]