Which equation is y=3(x-2)^2-(x-5)^2 rewritten in vertex form?

                y = 3(x - 2)² - (x - 5)²
                y = 3(x - 2)(x - 2) - (x - 5)(x - 5)
                 y = 3(x(x - 2) - 2(x - 2)) - (x(x - 5) - 5(x - 5))
                 y = 3(x(x) - x(2) - 2(x) + 2(2)) - (x(x) - x(5) - 5(x) + 5(5))
 y = 3(x² - 2x - 2x + 4) - (x² - 5x - 5x + 25)
                 y = 3(x² - 4x + 4) - (x² - 10x + 25)
                 y = 3(x²) - 3(4x) + 3(4) - (x²) + (10x) - (25)
y = (3x² - 12x + 12) + (-x² + 10x - 25)
                 y = (3x² - x²) + (-12x + 10x) + (12 - 25)
                 y = 2x² - 2x - 13
            + 13                + 13
         y + 13 = 2x² - 2x + 0.5
y + 13 + 0.5 = 2(x² - x + 0.25)
 y + 13.5 = 2(x² - 0.5x - 0.5x + 0.25)
      y + 13.5 = 2(x(x) - x(0.5) - 0.5(x) + 0.5(0.5))
      y + 13.5 = 2(x(x - 0.5) - 0.5(x - 0.5))
      y + 13.5 = 2(x - 0.5)(x - 0.5)
      y + 13.5 = 2(x - 0.5)²
          - 13.5         - 13.5
                 y = 2(x - 0.5)² - 13.5
I think?

That is so true, i can’t believe how true this is