The function \( f(x) = \frac{1}{2}(x - 11)^2 + 4 \) is a quadratic function in vertex form, where the vertex \((h, k)\) indicates the minimum point of the parabola (since it opens upwards due to the positive coefficient in front of the squared term).
From the form \( f(x) = a(x - h)^2 + k \), we see:
- \( h = 11 \)
- \( k = 4 \)
So the vertex of this function, which is also the minimum point, is at the coordinates \( (11, 4) \).
Since you're asking for the coordinates of the minimum point for a related square root function, let's consider the standard square root function \( g(x) = \sqrt{x} \). In relation to the quadratic function provided, we don't have enough information or context to derive a square root function directly from it.
The options provided do not contain the coordinate \( (11, 4) \) that we found, and thus it appears the options do not appropriately reflect the minimum point of \( f(x) \).
However, to directly address the options provided:
- (4, 11)
- (-4, -11)
- (4, -11)
- (-4, 11)
None of these coordinates match with the minimum point \( (11, 4) \).
If there’s an additional context or a specific square root function to consider, please clarify, and I will be glad to assist further!