https://www.desmos.com/calculator/asll5riedc

When this assignment was given to me, I was so excited to begin. At first, I had no idea what I wanted to create. My greatest option was to just browse the internet, and so I stumbled upon this image:

It gave an edgy aesthetic, which I kind of liked. The first thing I noticed was that it had a lot of short lines used for eyebrow and eyelash details. I decided that it would take way too long to create every line, so the idea of inequalities was brought to my attention. My plan was to shade in the eyebrow regions as well as the eyeliner regions. After planning out the general final look of this project, I started graphing on DESMOS. The first thing that I did was make the frames of the eyes. I did this step first because the frames of the eyes shape the entire look, so I had to get this step right. My next step was to graph the eyeballs. To be honest, I had trouble figuring this part out. I required assistance from Mr. Salisbury when I realized I didn’t know how to graph translations for the circles. I also struggled with setting the correct restrictions on the circles so they fit inside the eye frames. In the end. the solution was to graph the exact same circle twice and set two different restrictions so they overlap. That was my main challenge during the graphing process.

For my drawing, I used quadratic equations the most. This is most likely because my image consisted of many eyelashes and generally “round” lines. Quadratic equations were the easiest to use because their curves could be easily altered to fit the drawing I was going for. The second most used equation would probably be the linear equation. Although it may seem like my drawing doesn’t include many (if any) straight lines, it actually needed many short straight lines to connect the curved lines. The linear equation, much like the quadratic equation, was easy to manipulate, since the equation itself is simple to understand. Lastly, another equation – actually, *relation* – that I used quite a bit was the circle relation. Like I mentioned previously, I used it when graphing the eyeballs. However, it also came in handy when making curves that circled more than 180 degrees, which was difficult to do without graphing circles. Other than these equations (and relation), I also used a couple of trig functions and reciprocal functions. These were only useful in certain situations; for example, I used the reciprocal function for the nose and the trig function for a lip. This was simply because these functions perfectly captured the curves that I was trying to achieve for these specific features. Unfortunately, I did not get around to using cubic equations, square root functions, or exponential functions.

As I learned from Pre-Calculus 11, translations were graphed by adjusting the *p* and *q *variables in the quadratic equation. I became very nit-picky with the translations, as each line had to be perfectly aligned with one another. All of my equations had numbers like “2.7384” going all the way into the ten thousandths to make sure it was precisely graphed. This was also the case for vertical or horizontal extensions or compressions. Eyelashes took a long time because I tried to get each eyelash parabola compressed or extended to a perfect degree. With graphing, I did not really use any strategies, unless you count copy and pasting a strategy. When graphing many lines that were similar, like eyelashes per se, I would copy and paste one equation over and over and then simply alter that one equation. This reduced a ton of time for me.

Just for fun, I decided to add on to my original image plan and create a nose and mouth. This was just an impulse decision, and I completely eye-balled the entire thing. (I believe I forgot to mention this earlier, but I also technically eye-balled the eyes as well, because I was dumb and didn’t know I could paste my image into DESMOS and use it as a guide.) Either way, it was very fun to graph on an online program for the first time. The process was so engaging that every time I began to graph, I wanted to continue even after the class was over. I learned/reviewed how to translate graphs, compress/stretch circles, use inequalities to shade in areas, and use restrictions to determine where lines begin and end. This project was an extraordinary and awesome way to end our math year. I genuinely enjoyed learning how to graph images on DESMOS, and I might continue creating fun graphs and exploring the possibilities of functions and equations.