Answer
The arrows indicate the direction of motion.
1. A portion of the curve is in the first quadrant for $t8$
2. A portion of the curve is in the second quadrant for $-3
Work Step by Step
We find the $y$- and $x$-intercepts by solving the following equations:
$x=t^2-9=0$ ${ }$ and ${ }$ $y=t^2-8t=0$.
So,
$(t-3)(t+3)=0$ ${ }$ and ${ }$ $t(t-8)=0$.
So, the $y$-intercepts are $t=-3$ and $t=3$. The $x$-intercepts are $t=0$ and $t=8$.
Based on these intercepts we draw the direction of motion. From the graph it shows that
- a portion of the curve is in the first quadrant for $t8$
- a portion of the curve is in the second quadrant for $-3
