# Desmos Graph Picture

Sword, Shield, and Skyward Crest from *The Legend of Zelda*

https://www.desmos.com/calculator/3bgwyqs6ti

For many of the triangles, I used absolute value for symmetry and more concise equations (as I could use one equation in the place of two). I used linear equations as a base or for simpler lines such as the blade of the sword. Parabolas/quadratic equations were used for large curves and even was used to make sure the ‘wings’ were symmetrical and lined up in a curve. Square root function was used for the top of the shield. I used reflection, horizontal shifts, stretches, and expansion/compression to make small adjustments and to make sure not every curve was identical (an example of this is the bottom of the hilt handle or the inward curve of the top wings). I also used restrictions for absolute value, shading, and general neatness.

I was expecting challenges going into this project, but there were surprisingly few issues and I caught on to the flow of the project pretty quickly. Some small issues came up when shading the wings because there are so many different pieces, but if an equation didn’t work I simply split it into two smaller sections. I didn’t need that much help except for a few moments of jumpstarting a solution for shading or reflecting square root functions.

Something new I discovered was absolute values. It was an accident; when I was typing a square function, I hit x twice. Apparently \sqrt{xx} is the same as y=|x| . I went to Mr. Salisbury with my discovery, and he explained absolute values to me and what limited them does.

My main strategies included experimenting, symmetry, and duplicating lines such as parabolas to keep both sides lined up. Especially in shading, this made work simpler as it was reflecting and limiting instead of writing a new equation, and in some cases, due to absolute value, the shading was put on both sides.

Overall, this project gave me room to experiment with different graphs and see in action what part of an equation changes the pieces of the graph. It simplified the different functions as I got the hang of where to put <, |x|, 1/2x, 2x, square roots, and exponents in order to change graph types, reflect, stretch, and transform lines.