I genuinely don't know what the point is of the table, where do you use it for?
P-5=3s-15 because Pete is 20 and Sam is 10. 20-5= 15 and 3(10)-15 also equals 15. The answer is C.
The function in vertex form is

(refer to your other post I solved it there).
The general form of quadratic equations in vertex form is

, where (h, k) is the vertex of the parabola.
Here, a = 1, h = -6 and k = -54
Therefore, the vertex is (-6, -54) and it is a maximum because a = 1 is postive.