Write the equation of the curve z=x^4 - 2x^2 parametrically in 3 dimensions

Question

anonymous · Answer

please :(

e.mccormick · Answer

What is that?  Vector calculus?

anonymous · Answer

yeah something like that we have to rotate around the z-axis after but i capable of doing that just have no idea what it means by writing it parametrically, do you have any idea?

e.mccormick · Answer

A parametric equation shows it as a set of variables. As in parameters = parametric. Lots of examples: http://en.wikipedia.org/wiki/Parametric_equation

e.mccormick · Answer

Here are some calc2 and calc3 examples: http://tutorial.math.lamar.edu/Classes/CalcII/ParametricEqn.aspx http://tutorial.math.lamar.edu/Classes/CalcIII/EqnsOfLines.aspx

anonymous · Answer

yeah thanks i looked at all those websites, they dont have a 3 dimensional example :L

anonymous · Answer

but thank you for your assistance :)

happinessbreaksbones · Answer

I'm so sorry, I really want to help you. But I just cant :( 
maybe these people can help you..

@hartnn @psymon @dumbcow @Callisto

anonymous · Answer

all good, thanks anyways :)

happinessbreaksbones · Answer

@thomaster

dumbcow · Answer

looks like "z" is only a function of "x" thus you cant say anything about y(t)
let 
x(t) = t
z(t) = t^4 - 2t^2

anonymous · Answer

wow thanks heaps and in order to rotate this function around the z-axis i just use matricies right?

anonymous · Answer

and sorry was there a reason why we put it in terms of t and get x(t)=t
if you are too busy to answer i just wanted to say I really appreciate it!

e.mccormick · Answer

That is the parametric part. When you solve a system and there is more than one possible answer, you put the free variables as t or s and put the others in terms of them. http://freetext.org/Introduction_to_Linear_Algebra/Systems_Linear_Equations/Parametric_Solution/