Answer
$y=x^{2}(x-2),\ \ x\geq 0.$
Work Step by Step
From the parametric equation for x,
$x\geq 0.$
From the parametric equation for y,
$y=(t^{2})^{3}-2(t^{2})^{2}\qquad ...$substitute $x$ for $t^{2}$
$y=x^{3}-2x^{2}\qquad ...$ include the restriction for x
$y=x^{3}-2x^{2},\qquad x\geq 0.$
$ y=x^{2}(x-2)\qquad\Rightarrow x\geq 0.$
To graph, create a function value table using values for t, in ascending order of t, calculating the x- and y-coordinates of points on the graph.
Plot and join the points obtained with a smooth curve, noting the direction in which t increases.
