“Three Billboards Outside Ebbing, Missouri” provides a fascinating glimpse into the hardships faced by a hard-scrabble woman named Mildred (Frances McDormand) as she confronts the brutal murder of her teenaged daughter.

As an actor, McDormand has never been one to shy away from roles that made her look unattractive. If you saw her in the television mini-series “Olive Kitteridge,” owning the things that made her unappealing (like no make-up and wrinkles) became as much a part of her character as her spiteful tongue and quick wit.

McDormand takes that self-knowledge to the next level in “Three Billboards” as her character makes decisions that will upset the status quo and leave the landscape littered with unfortunate souls who stand in her path. McDormand outdoes herself in creating the subtleties of Mildred’s complicated personality. Drawing sympathy on the one hand and repulsion on the other, what Mildred does is not as important as the force behind her actions. 

Mildred is on a mission. After a year, the Ebbing, Missouri, police have failed to solve her daughter’s murder, and Mildred is tired of their inaction. To call attention to their lack of dedication, she rents three billboards on a country road just outside of town. This road is not one frequently traveled, so the billboard rental price is cheap. One of the billboards graphically describes what happened to her daughter. A second one asks why no arrests have been made. The third asks the man in charge directly: “How come, Chief Willoughby?”

Chief Willoughby (Woody Harrelson) doesn’t take the criticism lightly. For his ultra-conservative, not-too-bright deputy Dixon (Sam Rockwell), the billboards are cause for all-out war. By Dixon’s reckoning, he’s completely justified to toss Red Welby (Caleb Landry Jones), the man who leased Mildred the signs, out a second-story window. 

Mildred will grow more incensed with every passing day. She does not suffer fools lightly, and she’s quick to act with that singular sense of rage that only pure revenge can generate. Mildred’s unorthodox tactics will cause great consternation to Chief Willoughby and to the people who respect him.

Mildred’s own guilt associated with the last conversation she had with her daughter often consumes her. At its depth, it influences her relationship with her son Robbie (Lucas Hedges), who has to live with his mother’s eccentricities. Psychologists could have a field day.

As emotions heighten, Mildred proves relentless and steadfast in her resolve. Her singular purpose steels her against others’ judgments, her own culpability, and an unexpected turn of events.

Against it all, Mildred will survive. One intense situation at a time. One day at a time.

Rated R for violence, language throughout, and some sexual references.

Marilyn Robitaille has been writing film since 1999.