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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

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    $\begingroup$ This is a rather basic quartic function in $x$. Do you know how to graph polynomial functions? $\endgroup$
    – Andrew Chin
    Feb 27, 2021 at 6:19
  • $\begingroup$ For interest's sake, this function in $x$ can be rearranged as $y=1-(1-2x^2)^2$. $\endgroup$
    – abiessu
    Feb 27, 2021 at 6:24
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    $\begingroup$ 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. $\endgroup$
    – Rhino
    Feb 27, 2021 at 6:25
  • $\begingroup$ @Rhino Arg why didn't I think of that ,thanks alot .Could you copy paste that into an answer? $\endgroup$
    – Glowingbluejuicebox
    Feb 27, 2021 at 6:30
  • $\begingroup$ 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.??? $\endgroup$
    – trancelocation
    Feb 27, 2021 at 6:34

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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.

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