This exploration [url=https://www.geogebra.org/m/ptek2nwg]follows another activity[/url] about using curve stitching to introduce parabola as the shape of a quadratic graph. [br][br]In this activity, you may compare parabolas / quadratic graphs generated by curve stitching along two fixed lines. [br][br]For beginning learners of quadratic graphs, a simple activity could be identifying changes in the coefficients among a set of graphs (or family of graphs / functions). [br][br]More advanced learners may explore the relation between the coefficients: describe and test the relation, or even prove it.[br][br]You may try [url=https://www.geogebra.org/m/ry4nc2jh]another extended activity[/url] where the generating lines can also be varied.

By modifying the stitching in a fixed direction, a family of curves can be obtained. [br][br]This corresponds to a set of related quadratic graphs where 2 coefficients are varying in some particular ways.[br][br]For beginners, they may simply concentrate on the increase / decrease of these coefficients and identify corresponding features of the graphs.[br][br]For advanced learners, this can be an investigation about how these varying coefficients are related algebraically. [br][br]In this example, instead of common use of sliders to quickly change the coefficients of a single graph, I choose to display a set of graphs simultaneously to reveal the pattern both in the graph and the expressions before generalising with further (mysterious) symbols, or so called parameters.[br][br][br]