Question

sketch and identify the curve defined by the parametric equations
(I). y=t+1 (II). x=t^2-2t (III). -4_< t _<6

Answer 1

$y=t+1,x=t^2-2t, -4\le t \le6$

$t=y-1, x=(y-1)^2-2(y-1)$

$x=y^2-4y+3, -3\le y\le7$

This curve is parabola with a vertex at a point $(-1,2)$