Transforming y=x^2
I haven't shown any of the equations involved. My idea here was simply to show what the different transformations are: for example, a horizontal shear may look like a rotation, but it isn't.
I wonder if the absence of equations will encourage you to look for patterns?
Can you find any of the equations yourself?
Geometry people: can you find the focus and directrix of any of the transformed curves?
Calculus people and sneaky algebra people: can you find tangent lines?
Linear algebra people: can you quickly rule out some of these as linear transformations, and find matrices that describe the others? What are the eigenvectors and eigenvalues?