Welcome back, everyone. So in this example, we're going to take a look at this equation, y=2x3, and we're going to write 2 sets of parametric equations that describe this rectangular equation. So in other words, they want us to parameterize this y=2x3 equation. So let's take a look at the steps of how to do this. The first thing you're going to do in these problems is you're going to have to define t unless it's given to you already. In this case, it's not. So in this case, what we're going to have to do is choose a t to parameterize our equation, and there's always some guidance to this. In this case, you can always just try t=x or t=x equals whatever the thing in the parentheses is if you're given some kind of a parentheses in the equation. And in this problem, we're not told that we can't use x=t or t=x. So option 1 is that we just choose x=t or t=x. Right? So if we let t=x, then the second step is we're going to have to solve for x(t). So in other words, we're going to have to get x in terms of t. And if t=x, so you just flip the equation around. In other words, x(t) is just equal to t itself. That's the first equation, the first parameterized equation. Now to get the y equation, we're just going to have to plug that x(t) into the original equation for x. In other words, the y=2x3. And let's go ahead and do that. So if x(t) is equal to t itself, that means that y is equal to 2. And instead of now plugging in x cubes, we're really just going to replace this with t3 because that's what x is equal to. Right? So in other words, this really just becomes 2t3. Alright? So this is your x(t) equation, and this is your y(t) equation. So again, it's always kind of silly how these problems work out because if they're not if you're not told that you can't use this option or this definition of t, then this is always a viable set or a solution to your parametric equations. You can always just basically replace x with t, and then your y equation just becomes the original equation, but just you've replaced x with t. Alright? So that's always one of your options. So that's one of your sets of parametric equations. Or what we can also do is we're going to have to pick another sort of definition for t and sort of parameterize the equation a different way. Remember, there's always a ton of different ways that you can do this. There's no really correct answer, but there are some easier ones, for defining t. Alright? So let's go ahead and take a look at the second one here. You're going to define t unless it's given to us. In this case, we can't use t=x, obviously, because we just use that in the first one. So let's just try to pick a different definition for t. What we can do here is whenever you're just exhausted with you know, t=x or whatever the parenthesis is, you can start to just try to set t in terms of powers of x if you have t if you have powers of x. And so, again, so what you can do here is you can set t=x3. You always want to avoid even powe
Table of contents
- 0. Fundamental Concepts of Algebra3h 29m
- 1. Equations and Inequalities3h 27m
- 2. Graphs1h 43m
- 3. Functions & Graphs2h 17m
- 4. Polynomial Functions1h 54m
- 5. Rational Functions1h 23m
- 6. Exponential and Logarithmic Functions2h 28m
- 7. Measuring Angles39m
- 8. Trigonometric Functions on Right Triangles2h 5m
- 9. Unit Circle1h 19m
- 10. Graphing Trigonometric Functions1h 19m
- 11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m
- 12. Trigonometric Identities 2h 34m
- 13. Non-Right Triangles1h 38m
- 14. Vectors2h 25m
- 15. Polar Equations2h 5m
- 16. Parametric Equations1h 6m
- 17. Graphing Complex Numbers1h 7m
- 18. Systems of Equations and Matrices1h 6m
- 19. Conic Sections2h 36m
- 20. Sequences, Series & Induction1h 15m
- 21. Combinatorics and Probability1h 45m
- 22. Limits & Continuity1h 49m
- 23. Intro to Derivatives & Area Under the Curve2h 9m
16. Parametric Equations
Writing Parametric Equations
Video duration:
4mPlay a video:
Related Videos
Related Practice