As a noun:
* The students organized a petition to the principal demanding more recess time.
* The environmental group gathered thousands of signatures on their petition to stop the oil pipeline project.
* The court received a petition for divorce from the estranged couple.
As a verb:
* The activist group petitioned the government to pass stricter environmental regulations.
* The workers petitioned their employer for a raise in wages.
* The homeowner petitioned the city council to approve a permit for their home renovation.