Parametric Equations?

Question

A particle movies in a plane so its x and y coordinates vary with time according to the equations:
x=.5 * t^3 - 6t and y=.5 * t^2

I need to eliminate the parameter which I found to be:
x= (√2y) * (y-6)

I need the general form of this equation because I need to sketch the curve. Please show all of the work.

Answer 1

y = .5 * t^2 => t = +or- √2y

So x = . 5 * t^3 - 6t
= t(.5t^2 - 6)
= +or- (√2y) (y - 6)

I think the +or- is important because given the same value of y you can have two values of x corresponding to different values of t.

Answer 2

Quickest way may be to make a spreadsheet and get values for x and y corresponding to t = -1 through 10. Plot them ans see what you get