Here’s an idea that came to me in Anne Watson’s plenary today at the MEI conference in Keele. I think it’s quite challenging but I haven’t used it with any classes yet, so have no idea really!
I expect students to think of translating the graphs along x and y so that the turning point ends up at the origin. Then they can test whether y = x² . What other methods might you use? What other prompts might you give to learners that are stuck? What additional questions could you ask?