To create a self-portrait in Desmos, I utilized various graphs to represent different features of my face. For instance, I employed circles (equation: (x-h)^2 + (y-k)^2 = r^2) to model my eyes and the small mole on the side of my lip, taking advantage of their circular shape and symmetry. Additionally, I used ellipses (equation: (x-h)^2/a^2 + (y-k)^2/b^2 = 1) to create the flowers, leveraging their symmetrical and elliptical shape.

I also utilized parabolas (equation: y = ax^2 + bx + c) to model my eyebrows and hair, as they possess a curved shape that can be accurately modeled with a quadratic function. Furthermore, I employed lines (equation: y = mx + b) to outline my facial features, as they are straight and can be effectively modeled with a linear function.

To add a touch of realism, I used radical equations to create my lashes, taking advantage of their curved shape. I also employed cosine and sine functions, along with their inverses, to generate my curly hair. Moreover, I utilized hyperbolas to form my neck, showcasing the versatility of Desmos in modeling various shapes.

When selecting functions to represent different features of my face, I considered the shape and symmetry of each feature. I chose circles for their circular shape and symmetry, ellipses for their symmetrical and elliptical shape, parabolas for their curved shape, and lines for their straight shape.

I selected these functions based on their ability to accurately model the shape and symmetry of each feature, as well as their ease of use in Desmos. By combining these functions, I created a detailed and accurate self-portrait, demonstrating my understanding of mathematical concepts and their practical applications.

In this project, I explored the use of various graphs to represent real-world objects, analyzed the symmetry and shape of facial features, and applied mathematical ideas to create a self-portrait. I utilized reason and technology to select appropriate functions and model my face, showcasing my understanding of mathematical concepts and their practical applications.

I was able to enhance my self-portrait by experimenting with different colors, line styles (such as dashes and dots), and even animating certain features using Desmos’ built-in animation tool. Furthermore, I discovered how to create a degree sign in Desmos using “btheta” and applied that function in animation mode, pushing the boundaries of what is possible in Desmos.