Parametric

Investigations

by Molly McKee

Investigate

with varying a and k

When a changes the image gets larger or smaller, but retains the same general shape. Therefore we know that a is a scalar of the equation. The graph becomes more interesting as k fluctuates.

If k equals an even number, say 2, we can see that the graph again begins to look like a flower centered around the origin. The number of ‘pedals’ on the flower are still 2k, but the placement is different; in this graph the ‘pedals’ straddle the x-axis and the y-axis. The same differences and similarities can be found when k is odd and when k is a fraction.

k = .15

a = 1.5

k = .75

a = 1.5

k = 1.15

a = 1.5

k = 1.35

a = 1.5