Here is another family of graphs sent in by Andrei from Rumania
together with his solution to this problem. Can you find the
equations of the graphs in Andrei's illustration?
These challenges, together with the two challenges
More Parabolic Patterns
, develop the ideas of transformations
of graphs and the corresponding equations.
The illustrations give families of graphs, all of parabolas, formed
by reflections in the $x$ and $y$ axes and in the line $y=x$,
together with translations and stretches parallel to the
You are not expected to plot and join points although it is helpful
to consider where the graphs cut the axes. Rather you should think
of the features of the graphs and the effects of the