sketch

[logistic_guy]

Sketch.

$\displaystyle \bold{r}(t) = (t + 1)\bold{i} + (t^2 - 2)\bold{\bold{j}}$

 

[logistic_guy]

We can write this curve in terms of $\displaystyle x$ and $\displaystyle y$ if we are smart enough. Then, it is a piece of cake to recognize its graph!



$\displaystyle x = t + 1$

This means:

$\displaystyle t = x - 1$

This gives:

$\displaystyle y = t^2 - 2 = (x - 1)^2 - 2$

This is just the graph of a parabola that is shifted one unit to the right and two units downward and concaves upward with its vertex at $\displaystyle (1,-2)$



Since this is a parametrized curve, we expect it contains a path. It should be counterclockwise in this case. Why? Think about it!