7.1 Parametric Equations

[STARTS AT 14:08]

Instructor: Our last question, find two pairs of parametric equations to represent this graph, so y equals 2x squared minus 3. The easiest choice is x equals t, which would then make y equal to 2x-- no longer x-- 2t squared minus 3. That is one way to write that as a set of parametric equations. 

For the second, we really aren't restricted by anything. So I just went ahead and did something like this-- 3t minus 2. If we take x equals 3t minus 2, well, let's substitute that into the other equation. That will be 2x-- don't do that yet-- squared minus 3. 

If I replaced that with 3t minus 2, that would be 9t squared minus 6 minus 12t plus 4, minus 3. And we would have 18t squared minus 20t plus 5, once we combine those terms. 

And so this, these two together, would be my set of parametric equations to represent that. Now we haven't given any restrictions on t. That's one thing to note. 

It's because we're not giving anything. We're not t is between 0 and 2 pi, or anything like that. Then we can use whatever we want to rewrite those. 

[ENDS AT 15:44]