Graphing Functions in n Dimensions, Parametric Equations

[TheDemx27]

So I was watching this video on Khan Academy, and it talks about graphing functions that have values in multiple dimensions. It shows how to represent a linear function in 3 dimensions with a set of vectors, L ={p1 + t(p1-p2)|t∈R} where p1 and p2 are vectors that lie on the line you want to graph. My question is: How would one go about graphing polynomials, or trigonometric functions?

The video was under the linear algebra category, but to be honest I don't know enough about linear algebra to determine whether or not this should go in that subforum.

 

[Stephen Tashi]

My question is: How would one go about graphing polynomials, or trigonometric functions?

Having watched the video, I'd phrase your question this way:

A line can be represented in vector form as $L = P + tV$ where $P$ and $V$ are constant vectors and $t$ is a parameter. What curves can be represented using constant vectors and a parameter?

That's as good question. We could start by looking by plotting examples in 2D, like $C = P + tV + t^2W$ just to see what they look like.