In the beginning of this project, we went through various problems involving projectile motion, volumes, area (area diagrams), the Pythagorean theorem, etc. to learn about quadratic functions as well as how to solve the different variations of the functions. It first started with a rocket's projectile in a firework's show, which included all of the main parts of a quadratic equation and introduced the shapes of parabola curves on a graph. With more worksheets, we practiced rewriting different expressions into three forms, vertex, standard and factored form, while also finding the missing variables in different examples of real life problems. We learned of a parabola's vertex, x and y-intercepts, slope values, as well as what a negative can change in certain parts of the equation (the placement of points/overall position of the parabola and whether the arch curves downward or upward). Some of the equations we gathered were y=a(x-h)^2+k as well as y=ax^2+bx+c, which are the same thing but simplified/expanded
For the postcard project, we had to make a 4 x 6 postcard including quadratics, the purpose being to figure out why we learn quadratics in school by using examples of real life application. Individually, we all researched questions about questions and examples of quadratics and tried to prove it through what we learned throughout the duration of the project in a small diagram. It could be about anything we were interested in as long as it included quadratics to a certain extent (like more complex concepts of quadratics, trajectories, shape curves, etc.).
For my question, I thought of the starting parabola of a Pringles Stack Ring and figured that it was a good enough challenge as well as an interesting question to solve. Some things that went well were the fact that I could be able to solve the problem on my own without much help and I successfully solved the question with an example picture, going an extra level by scaling the picture rather than creating a Pringles Stack Ring myself (I felt like it was a bit unnecessary to make it). It was a fun challenge and an interestingly pointless question to consider. What didn't really go well was trying to accurately portray my reasoning and process in a simpler, more-visuals-than-words way in my postcard. Although I'm still proud of how it came out. In the beginning of this project I had a lot more interestingly pointless questions that I also wanted to do, like the parabola of the back curves of animals, a full moon cycle, etc. If I could do this project again, I would attempt one of the other questions or try to create my own Stack Ring and use those to solve the question I chose.