Question

How do you sketch the curve reprsented by the parametric equations : x=t2-6
y=1/2t-1?

Answer 1

pick some values for t, calculate x and y, and plot the points. Nothing hard about that.

You can tell it will be a parabola, since you already figured out that

x = (2y+2)^2 - 6

Answer 2

I guess you might mean:
x = t^2-6
y = .5t - 1
?????
if so, just substitute
2y = t -2
t = 2 y +2
then
x = 4(y^2+2y+1) -6
x = 4y^2 + 8y - 2
sketch that parabola