Challenge Level

The illustration shows the graphs of twelve functions. Three of them have equations

$y = x^2$

$x = y^2$

$x = -y^2 + 2$

Use a graphic calculator or a graph drawing program to sketch these three graphs and then to locate them in this illustration. Use the clues given in this information to help you to find the equations of all the other graphs and to draw the pattern of 12 graphs for yourself. For your solution send in the equations you have found with an explanation of how you did it.