I drew the function y=x^2, which is the parent graph and the one in black. I made five different transformation to the original one. I made a horizontal shift 3, to the right in green. And a vertical shift 2, downwards in blue. I combined the two translations to get y=(x-3)^2-2, which is in red. I then, made a reflection of the graph, which is basically a transformation over the x-axis.
During back to school night, I taught my mom how to make the same y=x^2 graph, but with different translation. The first thing I told her to do was to trace the parent graph on a patty paper, immediately she recognized it as a parabola. I taught her how to do a vertical and horizontal shift and how to read the functions. At the end i was surprised she actually understood all of it. Throughout my whole life, I had always asked my dad for help on homework, i guess i should ask my mom more often.