Are you sure? Here in Germany the basic fact that the two solutions of a quadratic equation must multiply / sum to the two coefficients is taught in high school, but I mean this is only useful for small numbers that are easily factorized.

But the more useful and well-known quadratic formula is always derived with “completing the square”, not the method described in the article (which I think is quite neat). Especially since I would suspect many students never really grasp “completing the square” and just skip to memorizing the quadratic formula.

I also learned this graphically as the roots are symmetric intersections of a parabola with the x-axis equidistant from their average.

and yet you don't produce an older link to back up your claim.