Answer
See image:
Work Step by Step
Build a table of coordinates (x,y)
$x=f(t)=1-t^{2},\quad \qquad y=g(t)=2t-t^{2}$,
Plot the points and join with a smooth curve.
Taking the initial t to be the left border of the interval, track the direction in which the points "travel" as t increases.