Hi Bongomash. Question 7.7 gives a quadratic function for the length of segment LM. That length is the difference between the two functions g and f at x. We find the difference by subtraction.
Write the expression g(x) - f(x), then complete the square. That will give the vertex form shown in 7.7
Question 7.8 asks about the y-coordinate of the vertex point (the maximum). I've assumed that they're talking about possible segments LM only where point M lies below point L.
If you're not familiar with completing the square or the vertex form of a quadratic polynomial, please let us know.
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