Marshmallows make awesome tools for math instruction!

A **catapult** is a device used to throw or hurl a projectile a great distance without the aid of explosive devices—particularly various types of ancient and medieval siege engines. Although the catapult has been used since ancient times, it has proven to be one of the most effective mechanisms during warfare. The word ‘Catapult’ comes from the two Greek words “kata” (downward) and “pultos” (a small circular battle shield). Katapultos was then taken to mean “shield piercer”.

There are many types of Catapults. In modern times, the word catapult can be used to describe any machine that hurls a projectile. This can include a slingshot used to hurl pebbles, a machine that launches airplanes off aircraft carriers, and of course, the ancient weapons of smash destruction!

**Gravity ^{2} + (distance) x (time)
**

Remember from algebra that the equation of a parabola is y = ax^{2} + bx + c. Also remember that when we handle these trinomials you were able to factor them to find the two binomials that when multiplied were equal to the expression. Lets’ use the value of -5t^{2} to represent the constant pull of gravity on our marshmallow. Now we need to determine how long the marshmallow was hurling through the air.

One of the advantages of having so many catapults in one place is all the data that becomes available to us. So the first part of our equation is -5t^{2}. Now we need to determine how long the marshmallow was hurling through the air. The average time in the air was 3 seconds and the average distance was 35 feet. If we look at the class data we can throw away the outliers and focus on the mean and median of the data. Using these numbers the average quadratic we can find is -5t^{2} + 17t.

How do we use this information? When we used the catapults for target practice we instinctively knew that we had to move closer or farther from the target. The starting point and the target became the roots of the quadratic equation!