Lesson 3: Parabolas & Functions & Catapults, oh my!

DO NOW

Can you think of any real world examples of parabolas? Where can you find that shape in the world? Be ready to share.

Examples

LEARNING TARGET

I can calculate the equation of a parabola in the real world in standard and vertex form.

I DO

One common source of real world parabolas is projectiles. A fun way to create a projectile is with a catapult!

Earliest known catapults were created in 4th century BC in ancient China. These were "traction" catapults.

Ancient Romans also used lots of catapults including this "Scorpio" catapult.

Catapult technology continued to develop for many centuries. Check out this counterweight trebuchet developed in 12th century Asia.

What shape does a projectile make between a catapult and the place it strikes?

WE DO

You will be creating your own catapult. Here is what you need to know:

Materials:

Tongue depressors

Wooden blocks

Clothespins

Plastic spoons

Wood glue

Bottle caps

Wooden platforms

You can use other materials, but they should not fundamentally change the scale or general ability of the catapult to keep the playing field level.

What should your catapult be able to do?

Launch a projectile from the catapult to a wall. There will be awards from the highest launch and the furthest launch.
Accuracy: there will also be an accuracy competition. Can you knock down specific targets?

The Assignment (The Graded Part)

Build a projectile. Gather data. Calculate information about your catapult's parabola. Create a visual representation of your results. This will be part of the "exams" grade.

YOU DO

You have a lot of flexibility about your visual medium:

Tri-fold display

Posterboard

Powerpoint

Edited video presentation

Something else?

We will work on these this week (Monday-Wednesday) in class. Competitions and testing will begin on Monday next week (10/18/21). You will present your projects later in the week to the class.

other helpful stuff

What data do you need to gather and how might you display it?

How can you find the vertex of your parabola?

It will be easiest to center your parabola on the y-axis so your vertex will be on the y-axis. Then, the coordinate of your vertex is going to be:

(0, max height of launch on wall)

Once you know your vertex, you know h and k.

The only other thing you need to know to write your equation in vertex form is a.

To find a, you will plug in a point that you know. An obvious point would be a x-intercept of your parabola, which is the place where your catapult was placed for launch. The coordinate of this location is (distance from wall, 0).

You will plug in this coordinate as (x, y), and your vertex as (h, k), then solve for a using:

y = a(x - h)^2 + k

How can you find the vertex form of your parabola?

How can you find the standard form of your parabola?

You can choose either metric (cm) or standard (in) units, but don't use both

I suggest rounding your measurements to the nearest whole number

What should i know about units and measurements?

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