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Coach is a seriously minor character in the book. He's the varsity basketball coach (no one in this book plays basketball) as well as the bio teacher. He's mainly here to provide a bit of assistance to the plot—he's the one who introduces the themes of sex and attraction with his squirmtastic and somewhat inappropriate approach to the human reproduction unit, plus he rearranges the seating chart, putting Nora and Patch together, which is how they meet.
Plot-practical purposes aside, Coach mainly serves as a reminder that adults aren't authority figures in the book. Students aren't afraid to joke around in his class, sass him, and even toss out innuendos. For example, when Coach explains that good scientific investigation takes practice, one student shouts out, "So does sex" (1.20). Coach "point[s] a warning finger" at the student, but that's all. The teenage voice and attitude dominates the classroom as it does the rest of the book. Take a look at the character descriptions of the Detectives, Mrs. Grey, and Dorothea as further evidence that adults are not major authority figures in the novel.