For this investigation I will explore the following equation:

for a=b, a<b, and a>b

Let us once again begin when a = b.







We see that when the numerator is 4 or more, it once again tells us how many petals we will have on our flower. If the numerator is 1 or 2, it still tells us how many petals we have but the graph shows us another feature that they have. It shows us that there is a double loop in each of these petals.

Let's look at a < b and a > b.









The column on the left shows what happens when a < b. We see that there is once again double petals around our flower. We see that in the right column the petals do not intersect at the origin. Look closer to follow the path of the green lines. Which petals are connected beside each other?

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