The word "vigorous" originates from the Old French "vigoureux" meaning "strong, robust, powerful."  This French term, in turn, comes from the Medieval Latin "vigorosus," which is derived from the Latin word "vigere," meaning "to be lively, flourish, thrive." The root of "vigere" is the Proto-Indo-European root "*weg-", which also means "to be strong, be lively".  

According to the Oxford English Dictionary, the word "vigorous" first appeared in English during the 14th, specifically around the year 1330..  It is found in the anonymous Middle English romance Arthour and Merlin. 

Examples of "vigorous" used in a sentence. 
"She shook her head in vigorous denial, and Angel and Doyle both glanced at her." 
"He was advised not to take vigorous exercise for at least a week." 
"Clyde was advised not to take vigorous exercise for a week, due to his recent injury." 
"Ethyl gave the cloth a vigorous shake to get rid of all the dust." 
"She remained vigorous into her nineties." 
"His speech was met with vigorous applause."
"She gave a vigorous defense of her beliefs."

Just the facts:

VIGOROUS Definition & Meaning - Merriam-Webster

VIGOROUS Synonyms: 207 Similar and Opposite Words | Merriam-Webster Thesaurus