to find the cordinates of the maximum or minimum point of a quadratic relationship?
Draw a graph, complete the square or set the derivative equal to zero.
It might help if we do a sample problem.
Suppose you have the relationship
y = x^2 + 2x + 5.
Rewrite that as the square of a monomial plus a constant.
y = (x+1)^2 + 4
The lowest value of y will be 4, when x = -1. Do you see why?