parabola net 1
This exploration follows another activity about using curve stitching to introduce parabola as the shape of a quadratic graph.
In this activity, you may compare parabolas / quadratic graphs generated by curve stitching along two fixed lines.
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).
More advanced learners may explore the relation between the coefficients: describe and test the relation, or even prove it.
You may try another extended activity where the generating lines can also be varied.
By modifying the stitching in a fixed direction, a family of curves can be obtained.
This corresponds to a set of related quadratic graphs where 2 coefficients are varying in some particular ways.
For beginners, they may simply concentrate on the increase / decrease of these coefficients and identify corresponding features of the graphs.
For advanced learners, this can be an investigation about how these varying coefficients are related algebraically.
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.