# How to graph $y=4x^2-4x^4$

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

• This is a rather basic quartic function in $x$. Do you know how to graph polynomial functions? Feb 27, 2021 at 6:19
• For interest's sake, this function in $x$ can be rearranged as $y=1-(1-2x^2)^2$. Feb 27, 2021 at 6:24
• 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. Feb 27, 2021 at 6:25
• @Rhino Arg why didn't I think of that ,thanks alot .Could you copy paste that into an answer? Feb 27, 2021 at 6:30
• So, you are online and asking how to graph a function given in the form $y=f(x)$ in the time of Desmos, WolframAlpha etc.??? Feb 27, 2021 at 6:34