In physics when learning simple harmonic motion they gave us the x coordinates dependence on time and similarly for the y coordinates
I got the resulting equation of path taken as $y=4x^2-4x^4$ which I have no idea how to graph
Is this a significant graph like the ellipse and hyperbola whose equation would be helpful to memorize .
Although to solve the question this graph is not required ,my query is just that if given this graph how would I plot it
You could just study it as a function: see where it equals zero, take the derivatives and study their signs finding local maxima/minima an then study it's behaviour towards infinity. This should give you all the informations about the graph.