Answer
Thus the curve is a parabola with vertex $( -1,0)$ that opens to the right.
Work Step by Step
The corresponding parametric equations for this curve are
$x$ $=$ $t^2$ $-$ $1$, $y$ $=$ $t$.
So, we can eliminate the parameter:
$t$ $=$ $y$ becoming to $x$ $=$ $y^2$ $-$ $1$, $with$ $y$ $\in$ $R$,
Thus the curve is a parabola with vertex $( -1,0)$ that opens to the right.
By comparing the different values of $t$, we can find the direction in which $t$ increases as indicated in the graph.
