Let K be a complete, algebraically closed nonarchimedean valued field, and let φ(z) ∈ K(z) have degree d ≥ 2. We study how the resultant of φ varies under changes of coordinates. For γ ∈ GL₂(K), we show that the map $\gamma \mapsto ord\left(Res\left({\phi }^{\gamma }\right)\right)$ factors through a function $ordRe{s}_{\phi }\left(·\right)$ on the Berkovich projective line, which is piecewise affine and convex up. The minimal resultant is achieved either at a single point in $P{¹}_K$, or on a segment, and the minimal resultant locus is contained in the tree in $P{¹}_K$ spanned by the fixed points and poles...