## Pre-Calculus Polar Graph Project

### Jianni Cariaga

My design is a flower. The flower consists of multiple rose graphs of different lengths for the pedals, and a circle graph is placed in the center. An infinity sign sits above the flower as a lemniscate graph.

a) In what ways did you experiment mathematically?

In this project I experimented mathematically in several different ways to create my design. I experimented mathematically by changing the 'a' values in my rose equations to determine the lengths of my flower pedals. In addition, I added several rose graphs of different lengths to give my design more detail. Lastly, I incorporated a circle and lemniscate graph to add a variety of polar graphs to my overall design. These are a few ways I experimented mathematically in this project.

b) What did you learn from doing this assignment?

I learned several things from doing this assignment. While completing this assignment I learned how to manipulate limaçon, rose, circle, and lemniscate graphs by substituting the 'a', 'b', and 'n' values to graph a desired sketch. As I created my design I became more familiar with each polar graph equation its variables. I gained a familiarity with polar graph symmetry and polar coordinates as well. These are several things I learned from doing this assignment.

c) Did you enjoy working on this assignment? Why or why not?

Overall I enjoyed working on this assignment. I enjoyed working on this assignment because it served as practice for graphing different polar graphs. With this practice I felt more confident when identifying or graphing polar graphs. I am also more comfortable finding the "key points" of a polar graph, when given its equation, to help me sketch it. This is why I enjoyed working on this assignment.