The equation given is in the vertex form of a parabola, which is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex of the parabola.
From the equation \( y = 4(x - 25)^2 - 61 \), we can identify that:
- \( h = 25 \)
- \( k = -61 \)
Therefore, the vertex of the parabola is \((25, -61)\).
The correct response is \( (25, -61) \).