** not count as grade **
By using the functions of circles, ellipses and hyperbolae, I created a self-portrait. For the face shape, I used several hyperbolae to make a symmetrical shape. I adjusted the values of the hyperbola function to create an angular shape for the chin as well.
For the eyes, I used both circles and ellipses. I combined ellipses with different values of the variables of the function and restricted the domain and range to create an almond shape. Then, I added the circle functions to represent the iris. I also used ellipses to create eyebrows and restricted the range.
For the ears, I used circles to represent the rounded parts of the ears, then connected them with the straight lines using hyperbolae. For the nose, I used the symmetrical lines from the hyperbola function. Then, I used ellipses for the sides and used the center of a hyperbola for the middle part of the nose.
I used hyperbolae and ellipses to create the shape of the mouth. I used the bottom half of ellipses for the bottom two lines and used a combination of hyperbolae to make the top lip. For the neck part, I used the hyperbola for two symmetrical lines and used parts of ellipses to create the clothing part.
Lastly, I graphed multiple hyperbolae to create the lines of the hair. I used different features of the function and its graphs, such as the straight lines or the angular/rounded center of the hyperbola.
Rubric extending explanations:
Explore mathematical ideas: For this part of the hair, I wanted to use the round part of an ellipsis, but it had to be at an angle to look smooth. I searched for how to incorporate angles in the function to rotate the shape of the graph. I was able to successfully rotate the graph by using sin and cos and using the slider feature in Desmos to select the right value for the angle.
Apply mathematical ideas using technology: I searched how to add and use custom colours in Desmos. I was able to use different unique colours for the graphs by creating equations with RGB values. This helped personalize my work.
Analyze mathematical ideas using technology: I coloured in the eyes by using inequalities for the functions of the circles. I combined several graphs of different functions to create a facial feature, rather than using one function for each part. This helped make the portrait more realistic, such as making the shape of the eyes, nose and mouth.
Core competency reflection:
I demonstrated both critical and creative thinking to complete this assignment. I had to learn about the different functions, the equations and what the different variables represent. Then, I analyzed how to utilize the different features of the functions to create recognizable facial features. I used creativity to combine multiple graphs together by using the technological features.