"Parabola" Function Machine

To help students understand the idea of "functions", the curriculum [i]Everyday Mathematics[/i] uses imaginary "function machines". But many geometric constructions are [b]rea[/b]l function machines, such as this construction that generates the parabola that has the formula [math]y=x^2[/math].

¿Por qué [math]v=u^2[/math]? Sugerencia: son semejantes, los triángulos [i]ABC[/i] y [i]PAC[/i].