Category Archives: Elective 3

Pre Calculus 12 Conics Project: Desmos Self-Portrait

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https://www.desmos.com/calculator/jncco0tlaz

For my self portrait I used many different types of functions: parabolas, hyperbolas, circles, and ellipses. I used a picture of myself as a base to make my features accurate and built my graphs on top of it. To put the graphs in the right places on my face, I used letters in the formulas as sliders. I quickly found that I was running out of letters, but solved this by entering the value of the slider in place of the letter in the formula. Doing this I was able to re-use letters and my functions were still in the right location and the right shape. I made the face shape from two parabolas which emphasizes the cheekbones and makes accurate chin and forehead proportions that could not have been achieved with an ellipses. My neck is two sides of a hyperbola to have a uniform length on both sides, because my face is not perfectly symmetrical one side overlaps with my chin. I chose to form my hair with parabolas to convey that it is not completely straight. My lips are made up of a mixture of parabolas, and two ellipses for the cupids bow. With the ellipses I was able to get a better, sharper curve for the top lips. The bridge of my nose is made of two sides of a hyperbola, the bottom with a parabola, and the nostrils with two restricted circles. These shapes help convey the unique shape of my nose. I chose to make my eyebrows and eyelids with parabolas because they are surprisingly parabola shaped, this can be seen if you un-hide my reference photo on the graphs. My eyeliner is made up of straight lines, I wish it looked that straight in real life, and my eyelashes are slightly curved parabolas. Finally for my eyes I chose parabolas for the inner corners, ellipses for the eye shape and irises, and circles for the pupils. I used all these to form an accurate shape of my eyes without pointy sections which I would have gotten with other functions.

I believe that I am extending in this project and went beyond the basic criteria. I used very exact measurements and restrictions for my functions and the features aren’t mirrored over the y-axis. This makes my graph look more realistic, nobody is perfectly symmetrical. I also found out how to use shading to fill in my shapes and filled in some very finicky sections like the lips and eyeliner. I used an online colour picker app to make all my lines the same colour as the features they represent. I found the RGB colour codes for my features from my reference photo. I think I went above and beyond in making the portrait realistic not just with functions, but with the use of colour as well.

A blurry and glitchy photo of my self portrait. I promise my lips and eyeliner are shaded in properly.

Core Competency Self-Reflection: Pre Calculus 12

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Option 1 – Collaboration

My group and I worked very well together this semester. We all contributed, even in small ways, to every problem we worked on and weren’t afraid to challenge each others answers or ask questions. We didn’t have definite roles in my work group, but I often took up the “scribe” role and wrote out the questions. Even then, we usually had a system where if the person writing didn’t know how to solve the problem or needed clarification on something, another would take the marker and talk through the answer. Often our whiteboard is filled with all three of ours’s writing. We work very well as a group.

The picture above is from the in class work questions from the polynomial unit for section 3.2, though this unit is more simple than others we had some difficulty with question 1. This was our first time working with a graph like this and we were all confused about what to put where and how to set up the basic shape of it. We combatted this by checking the notes and learned how to find the degrees of the x-intercepts and the graphs end behaviors. We ran into another problem when calculating points to plot, we got very large numbers that seemed unrealistic. With Ms. Eaton’s help we found that the numbers did make sense in the equation after using “Desmos” and seeing what the graph looked like. We solved this problem and many others utilizing all the resources we have been provided with.

I think my group’s problem solving skills could be improved in a couple of ways according to the Core Competency collaboration profiles. First off, I think our work and roles could be divided up a bit more equally according to profile 2. This includes not relying on a certain very much smarter member to do a lot of the work and have everyone try their best to solve the question without fear of getting it wrong. We can work together to get it right. Another way to improve our collaboration would be to talk to a few other groups if we are really stuck, according to prompts 4 and 6. Instead of looking at what the other groups are doing to solve harder problems, we should talk to them and ask them about their solving process. We do this already but I think we could do this even more and talk to even more groups than just a certain few.