To teach quadratics you can use Cavalieri's parabolograph: https://en.etudes.ru/models/conic-sections-cavalieri-parabolograf/ https://en.etudes.ru/models/conic

To teach quadratics you can use Cavalieri's parabolograph: https://en.etudes.ru/models/conic-sections-cavalieri-parabolograf/ https://en.etudes.ru/models/conic-sections-cavalieri-parabol... This may make all of the variables more "real" - but note that the equation graphed is really A(X - B)^2 = Y - C, where (B, C) is the vertex and A is the "setting" (clear if you examine the device. This is relatively similar to the complete-the-square formalism but with a straightforward geometric and "hands-on" interpretation.