Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 4 / 32E / b / i / Solution

The graph of $F$ is the symmetric tent with verticesIf $0<\mu <1$, then $F\ge 0$ andso $F^2$ is an upward-pointing V with its minimum at $(0,1-\mu )$ and equal endpoint values $1-\mu +{\mu }^2$.

If $1<\mu <2$, the zeros of $F$ are $\pm 1/\mu$ andThus its five vertices are