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 or 4, we can see that the graph begins to look like a flower centered around the origin. The number of ‘pedals’ on the flower are 2k. So when k equals 2 the flower has 4 ‘pedals’ and when k equals 4 the flower has 8 ‘pedals’.

The general appearance of the graph is the same if k equals an odd number, only the numbers of ‘pedals’ change. When k is odd then the number of ‘pedals’ equals k.

k = 3.125

a = 1.5

k = 3.625

a = 1.5

k = 3.875

a = 1.5

k = .05

a = 1.5

k = .75

a = 1.5

k = 1.05

a = 1.5

k = 1.25

a = 1.5

k = 2

a = 1.5

k = 3

a = 1.5

k = 4

a = 1.5

k = 5

a = 1.5