00:01
So here we have a curve that is a segment of a parabola, and we want to parametrize it with t, functions x and y of t.
00:11
In general, when we're parametrizing a part of a function f of x, the simplest way to parametrize it, as it were, is just going to be t, f of t.
00:25
This is our x is t, and our y is f of x, f of t.
00:29
It's not a super interesting parametrization much of the time, but it'll get the job done, and that's all we need.
00:35
It's just a matter of figuring out what the parabola is.
00:38
What we see, it goes through the points 0, 0, 0, and 2, 2.
00:43
So if it's of the form f of x equals ax squared plus bx plus c, then we should have c equals 0, of course, because when this is going through point x equals 0, we have y also equal to 0.
01:03
I'm also noticing that f prime of 0, which is equal to 2 times a times x plus b, this also looks like 0.
01:15
You can see a tangent line looking like that.
01:18
So b is equal to 0.
01:19
Really, it's just a matter of finding a.
01:22
Our point here, 2, 2, tells us that a times 2 squared equals 2.
01:28
So a should equal one half...