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### Course: Pixar in a Box > Unit 11

Lesson 1: Modeling grass with parabolas- Start here!
- Introduction to parabolic arcs
- 1. String art
- String art construction
- 2. Midpoint formula
- Midpoint formula
- 3. Parabolic arcs
- Parabolic curve matching
- 4. Modeling grass
- Design challenge: Modeling grass
- 5. Animating grass
- Design challenge: Animating grass
- Getting to know Tony DeRose
- Hands-on activity

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# 3. Parabolic arcs

Are we really creating parabolic curves using this construction? Let's gain some insight first.

## Want to join the conversation?

- Don't we already know that this is a parabola? Why is he questioning it?(1 vote)
- No, and in fact that's not obvious. There are a lot of curves that look parabolic, for example, circle arc, ellipse arc, logarithm, etc. They all have different equations. We're trying to prove that in our case equation would be quadratic.(4 votes)

- Does this video work on big iPads? Because it doesn’t seem to work for me.(1 vote)
- I did not understand any of the midpoint formula fro the last lesson when you answer the questions it didn't even tell me how to do it?(1 vote)
- it but it's really really really stressing me out (like, a lot). Do I really need to know all the technical stuff with animation? If I wanted to learn math, I would take a math lesson. I want to learn animation, so PLEASE if there's going to be any math just keep it simple. This is very confusing and stressful! I want to learn JUST animation! NOT math!(1 vote)
- This kind of animation has a lot of math in it. If you want to do a course that is easy math-wise, try the colors course.(2 votes)

- This is so confusing because theres alot of new pixar launguge its kind of like proggraming launguge but its not.This is so confusing.(1 vote)
- Are parabolic the same as relations and functions(1 vote)
- So about the last question on the previous excersice- Where was I supposed to get Mx from?(1 vote)

## Video transcript

(lamp and ball boinging) - Congratulations. You're now an expert on midpoints. (arrow whooshes) Now let's take the next step. I've been claiming that the curves created with the string art construction are parabolas. But how do we know that's actually true? Well, it's actually a little bit hard to prove that rigorously but we can get some intuition in the following exercise. Now you may have seen parabolic arcs as graphs of quadratic equations like this one, for instance. So here I have a green curve that's the graph of a quadratic function. And so it's a parabola. And I have a blue curve generated through the string art construction. It's my job in this exercise, it'll be your job in the exercise, to see if you can reposition the points so that the blue curve sits exactly on top of the green curve. So for instance, I'm gonna try moving this point, say down here. And this point over here. Over there. So the blue curve is getting a little bit closer, but it's not exactly on top of the green curve yet. And in fact I'm gonna ask you to try it in the next exercise.