[color=#6aa84f]This page continues an exploration discussed in another page:[br][url=https://www.geogebra.org/m/tqvq9ybk]https://www.geogebra.org/m/tqvq9ybk[/url] [/color]

The line and parabola are moved upward without changing their shape. We can now construct another triangle below it, on the x-axis for comparison. [br][br]A'and B' on the x-axis, directly below A and B, form the base of a triangle. The height C'D' is the same as the segment CD. [br][br]You may drag C to check how the two triangles vary together. [color=#ff0000]Can you explain why they should have the same area? [/color][br][br]Note carefully how D' changes and reaches its maximum height. You may right click point D' to turn on 'show trace' in the menu. Drag point C again and you will then see more clearly the path of D'. [br][br][color=#ff0000]How would you describe the path of D'?[/color]

In order to describe more precisely the path of D', you may refer to the functions of the line and parabola, which are f(x) and g(x). By creating another function g(x)-f(x), you should obtain a graph that gives that the path of D'.