Why use this resource?

This is an exercise in visualising pairs of quadratic equations. Students have the opportunity to develop their understanding of the symmetry properties of parabolas and how this can be linked to the difference of two squares. Students will find that sketch-graphs have a key role to play in this resource.


Some revision of transformations of graphs may be useful as a starter.

Possible approach

Encourage students to sketch each of the graphs and note what is the same and different about each graph and how this relates to the algebra.

Key questions

What’s the same and what’s different about these pairs of parabolas which have the y axis as a line of symmetry?

Possible extension

Can you generalise for pairs of parabolas that have the x axis as a line of symmetry?

A version of this resource has been featured on the NRICH website. You might like to look at some students’ solutions that have been submitted there.