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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

miracle173
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Glowingbluejuicebox
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    This is a rather basic quartic function in $x$. Do you know how to graph polynomial functions? – Andrew Chin Feb 27 '21 at 06:19
  • For interest's sake, this function in $x$ can be rearranged as $y=1-(1-2x^2)^2$. – abiessu Feb 27 '21 at 06:24
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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. – Rhino Feb 27 '21 at 06:25
  • @Rhino Arg why didn't I think of that ,thanks alot .Could you copy paste that into an answer? – Glowingbluejuicebox Feb 27 '21 at 06:30
  • 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.??? – trancelocation Feb 27 '21 at 06:34
  • @trancelocation I get this comment alot when I ask graphical questions here ,Desmos won't help in an exam where I can't use Desmos lol.This was asked in an exam where calculators of any sort are not allowed . – Glowingbluejuicebox Feb 27 '21 at 07:56
  • @Glowingbluejuicebox Then, you should clearly indicate this in your question. And if you get comments like mine "a lot", you should finally start studying how to graph functions. – trancelocation Feb 27 '21 at 08:59

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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.

Rhino
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