Are All Parabolas Similar? A Geometry Check with Parameters

This GeoGebra example visually demonstrates that the statement “all parabolas are similar” is not generally true: different parameter choices can change the parabolas’ shape in ways that cannot be matched by a single similarity transformation. The key math ideas are parabolic parameter dependence, similarity criteria (how parameters control the opening/scale), and geometric reasoning using transformations and constructed reference configurations. Construction-wise, it relies on GeoGebra’s polygon-based scaffolding via the command Polygon to build auxiliary geometric structures, then uses multiple coordinated objects (such as sets of points and labels like a, b, c, d, g1, g2, A/B/C/D, q1/q2, and the grouped variants b1/c1/a1/d1, plus points like x1 and text labels such as text1/text2) to compare the resulting shapes and highlight when similarity does or does not hold. Suitable for upper-secondary students learning coordinate geometry, graph transformations, and basic function geometry, and also for classroom exploration or worksheet activities aimed at testing mathematical claims.