In our final jump, the barbie doll was 3/2 foot away from the ground, therefore we failed to give our doll a thrilling experience. The reason why this happened is because our graphs weren't accurate, as we did not use a solid method of coming up with them and instead we guessed and checked our graphs. Moreover, it was a mistake to have chosen quadratic graphs to represent this situation as quadratic graphs have exponential properties but our rubber bands do not stretch infinitely. Furthermore, last time we plotted our trials/points in different equations, therefore there weren't enough trials per meter to make a mathematical graph.
So our group decided to redo our project and start from scratch.
Here is our data chart which was created by test jumping our barbie from various heights and finding out the amount elastics needed for that certain jump.
Here are some of our trial videos:
Height

Elastics used

1.75 m

11

1.92 m

14

2.60 m

18

3.25 m

20

4.17 m

31

5.20 m

37

Using this data, our group decided to use a computer program called geogebra to come up with a linear equation for the jumps. We decided to use a linear equation this time as we learned that quadratic equations didn't work as they included exponential properties and the rubber bands that we used for these jumps didn't. And another error that we made in the past was that the points that we got the the graph did not entirely represent a quadratic equation.
To get the equation we inserted this in our geogebra spreadsheet to plot the points.
The y axis represents the height of the jump and the x axis represents the amount of elastics needed for that jump.
Here is the process on how we managed to find our equation:
1. Open the spreadsheet in geogebra, and then type in the x, y, and the points. (Warning, "X" and "Y" have to be in quotations so it is not identified as a variable.)2. Then, in the input box at the bottom, type in "cellrange[C2,C7]" as the points that I would be using to make the bestfit line starts from the C column in the spreadsheet, from the 2nd row to the 7th row.
3. Then click on the input box, type in "fitpoly[list1, 1]" as I need to make the bestfit line for list 1, the points of C2  C7, and 1 because I needed a straight line.
This is the equation that we came up with:
y = 0.13x+0.28
Now that I got this equation, I believe that if we had applied this equation for our final jump, we would have gotten a better result, giving the barbie a more thrilling experience.
To prove that this equation is the right equation, our group did another final jump which went successfully the barbie doll did not touch the ground by about 10 cm which is better than the final jump that we did before which had a gap of 3/2 feet.
According to our equation, for our barbie to jump 5.94 meters, the we should use 43 rubber bands. We
based our jump on this information and managed to get a much more thrilling jump by making the barbie not touch the ground by a couple of inches. In conclusion, if we had not used a quadratic equation in the first place and used a more mathematical way of getting an equation for this project, we would have been more successful overall.
Reflection:
Overall, I believe that this project had a very positive effect on my learning as it has taught me how to use linear equations in real life, moreover it has also improved my problem solving skills by a lot as we had to deal with many problems while finishing this project. We faced problems such as, not being able to come up with a equation manually therefore we had to use programs such as geogebra to get a more accurate graph that serves our purpose in a better manner. I really want to thank my teacher Mr. Okness for giving me an opportunity to show my understanding in math in a real life situation which I never did before.