Final answer:
The correct answer to the pattern of adolescents' mood changes over time in the family context is called a curvilinear mood pattern, which is part of the broader concept of the family life course.
Step-by-step explanation:
The U-shaped or inverted-U pattern of results, as seen in studies that have examined how adolescents' moods change over time when with their families, is called a curvilinear mood pattern. This concept is part of the broader family life course, which is a sociological model that sees the progression of events in a family's life as fluid rather than occurring in strict stages. The term curvilinear reflects the idea that mood variations can rise and fall in a non-linear fashion, which is different from predictable mood swings or an emotional rollercoaster that suggests more extreme and less predictable changes in emotions.