Describe the curve given by the following equation please help

*its a vector equation with i,j,k components

r(t) = ti + t²j + 3k

Since z = 3, the curve is in the plane z = 3, which is of course parallel to the xy plane.

x = t, y = t²
gives
y = x² which is a parabola.
In the xy plane its vertex would be (0, 0) and its axis the y axis (x = 0)
but if we shift it up 3 units we have
parabola with vertex (0, 0, 3)
and axis the line x = 0, z = 3