Quadratic profile summary

profile_quadratic fits a least-squares parabola to at least three finite (parameter, objective) points. It requires positive fitted curvature, reports the vertex and minimum, and gives a normal-approximation interval using an inverse-normal approximation at the requested confidence.

The interval is a local quadratic approximation, not a constrained re-optimization profile over a model. Multimodal, asymmetric, or flat objectives can make it misleading or cause validation failure.