Sketching vector-valued functions

Sketch $\displaystyle r(t) = t^2i + t^4j + t^6k$

Attempt:

I tried to find a surface that this curve lies on so I said:

$\displaystyle x = t^2$ therefore:

$\displaystyle y = x^2$ and $\displaystyle z = x^4$

I then drew these surfaces, then tried to see what happens when t = large positive number and then a large negative number. I got that the graph lies in the first octant, but I am not sure where on the surfaces $\displaystyle y = x^2$ and $\displaystyle z = x^4$ the curve lies on (I learnt that you use these surfaces as a guide to draw the curve).