As Conics was our last unit for Pre-Calculus 12, instead of taking a paper exam, we were tasked to create a self-portrait in Desmos. For this assignment, we were required to implement 2 circles, 2 ellipses and 1 hyperbola, and then we were free to use various functions that we had learned throught Pre-Calc 12 to create our self-portraits.I first started out with my face shape as having done my face shape first has helped me outline where my other features, such as my eyes, eyebrows,ears, nose and mouth would be placed. For my face, since my face isn’t completely round, I decided to use an ellipse as i felt like it was most similar to my face shape. I used the formula: (x-h)^2/a^2 + (y-k)^2/b^2 = 1. After my face shape was complete, I then started working with my hair. For my hair, I first decided to add my side bangs first. As my bangs are not that noticeable and they part to the side instead of straight down my face, i decided to use radical functions and inverse it for the slight wave in my bangs. I did this by using the formula: y= a (√ x – b) + c. Afterwords, I graphed my nose by using a hyperbola with the formula: (x-h)^2/a^2 – (y-k)^2/b^2 = 1. After graphing the hyperbola, I added domains and ranges so that my graphing lines would match up with my pictures, which i used as a reference when doing this assignment. By adding domains or ranges to these functions, I am able to control how far or wide my function would be drawn. I then graphed my eyes by using ellipses and circles. I am able to show my expanded level of learning my adding small details in order to enhance my features further such as adding another pair of circles to show my eye’s pupil and also added earring to my ears. I also tried to show my expanded level of understanding with my ears as I feel like the ear shape I graphed above identifies with me better than graphing half circles for ears. Overall, although this project took a lot of time with experimenting with different functions and inputting different values into these variables, I found this conics assignment to be a fun and great project to end the course.
Desmos Self-Portrait Link