Draw a parabola using a pen attached to a robot

Theory

A parabola is a function (or mapping) $y=ax^{2}$ (without the constant). The inverse function of the positive root is $x={\sqrt {y/a}}$. We drive the robot in $5$ steps to the vertex.

Note that all parabolas are similar, see is only One True Parabola by Matt Parker

Exercises

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