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Phase 3

Our flower graph  has 4 pink petals that bloom. The pistil of the flower is surrounded with a blue ring, and has a 4-leaf clover in the middle of the pistil. The 4-leaf clover represents wealth and luck.

In Phase 1 we drew 1 rose, 1 circle, and 2 lemniscates. However, during the process we found 1 mistake in our equations and had to change our equations to fit the graph. We changed one of the lemniscate equations (#4) from r^2=4 cos 2 theta to r^2= -4 cos 2 theta. The graph in all did not change except for the equations.

Final Phase

A. We experimented mathematically when we found different graphs for the project. We found a lemniscate, rose, and circle graph. We found the equation of the circle graph by using the equation r=n, which n is a real number. Then, we found the equation of the rose graph by using the equation r=nsinp(theta). P is the number of petals and n is the length of the petal. If p were to be even then the number of the petals would be doubled. We found the last lemniscate graph equation by using the equation r^2=4cos2(theta) and r^2=-4cos2(theta). We used two different equations for the lemniscate graph so it would look like a rose graph.

B. While we were completing this assignment, we learned that we can make various kinds of graphs by combining different graphs together. We also learned how to find polar equations for the polar graphs. This project was helpful to us because it educated us in finding graphs with sin and cos.

C. We enjoyed working on this assignment because we created a beautiful graph together. It was very fun! Even though we had to take turns posting on tackk.com, it was very fun. We thought it was very cool how we could create a graph by just drawing it, but then finding the equation later on. We fixed the graph throughout the phases.

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