Every concept comes with something you can pull, drag and break. Read less, notice more.
Drag the bob and let go. The two bars trade places as it swings, but their total never moves — until you add friction.
drag the bob
Friction off. The two bars swap, but their sum stays at 100%. This is conservation of energy.
A formula is easier to trust once you have watched it fail. Move the sliders and push the curve until it stops working.
Lift the parabola off the axis and the two roots slide together, meet, and vanish. Watch the discriminant at the moment they go.