00:02
Okay, so for this question, it involves parametric equations.
00:08
And for part a, we are going to sketch the curve using the following equations.
00:16
X equals t squared and y equals t cubed.
00:23
In order to sketch these equations and indicate their direction, we will find the corresponding x and y values to t values so first off let's make a chart t x and y and now since it will be as t increases we will have to then make our t values as t increases so we go from zero one two three we can only do the first few points in order to get a general idea of how the graph appears.
01:08
So, starting off with zero, we'll plug in zero into our equations.
01:13
So plugging in zero for t, we get x equals zero and y equals zero.
01:19
Then plugging in one, we'll get x equals one and y equals one.
01:25
Next plugging in two, we'll have x equals four now, and then we'll have y equals to eight because two squared is four and two cubed is eight.
01:36
Doing that, following is 3, where we'd have x equals to 9, and then y equals to 27.
01:49
Now we have these four coordinate points, 0 ,1, 4, 8, and 927...