Does anyone know what the 'horizontal points' method of graphing a parabola is? If so, halp.

I need to explain how to use this method to graph a parabola for a project I'm doing. However, I have no idea how to explain it and as far as I know my teacher may as well have invented it because no one else seems to have ever heard of it. This is his note, if you can make any sense of it... The horizontal points business starts on the second page.