early 15c., from Old French investigacion (14c.), from Latin investigationem (nominative investigatio) "a searching into, a searching for," noun of action from past participle stem of investigare "to trace out, search after," figuratively "search into, investigate," from in- "in, into" (from PIE root *en "in") + vestigare "to track, trace," from vestigium "a footprint, a track" (see vestige).
word-forming element making adjectives from verbs, meaning "pertaining to, tending to; doing, serving to do," in some cases from Old French -if, but usually directly from Latin adjectival suffix -ivus (source also of Italian and Spanish -ivo). In some words borrowed from French at an early date it has been reduced to -y (as in hasty, tardy).
<a href="https://www.etymonline.com/word/investigative">Etymology of investigative by etymonline</a>
Harper, D. (n.d.). Etymology of investigative. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/investigative