I would like to discuss with everyone the difficulties in the properties of quadratic functions

For example, for the quadratic function y=2x2-4x-1, first, the quadratic term coefficient 2 is proposed, resulting in y=2 (x2-2x) -1
Then, formula the equation in parentheses by adding half the square of the coefficient of a linear term to x2-2x, resulting in y=2 ((x2-2x+1-1) -1, further simplified as y=2 [(x-1) 2} -1] -1, count y=2 (x-1) 2} -3.

Not math, but beauty!