177: Parabola and friends

Is it possible to choose four points on the graph of y = x² that are the vertices of a trapezoid?
A parallelogram?
An equilateral triangle?

Here's y = x² to help you think.

Is it possible to choose four pts on the graph of y = x² that are the vertices of a trapezoid? A parallelogram? An equilateral triangle?
— James Tanton (@jamestanton)