The task is to calculate the are of the shape formed by this curve:
$$y^2 = x(x-2)^2$$
Now, if I use Desmos to see what the graph looks like, I can do it. But if I get this question on my exam, I would not know what to do, because I could not visualise the curve. I'm in high school, so I'm not very familiar with such curves and I would like it if you can explain to me how to draw such a curve or perhaps, if it is possible to calculate the area without knowing what it looks like at all?