Should we think about it graphically, it will be no wonder that we should pay our attention to the points of the parabola intersecting the abscissa axis. In other words, we need our vertex to intersect the x axis only once per se. The vertex:
As a result, our is parametric. suits us because . If , we do not have any roots at all. We have two roots if .
Here's a diagram showing how to combine angles LDA (in red) and angle ADE (in blue). Hopefully it becomes a bit clearer why these two angles add up to line segment LE. Erase the shared segment DA if it helps show LE better.