The graphs of the equation are known as **roses**
with various numbers of leaves. Below are graphs of the above
equation with **a = 1** and varied values for **k**. It
appears that **k** affects the number of "petals"
of the graph. If **k is
odd**, then there are ** k petals**.
If

Notice that when **k** is odd, there is
always one petal that "lies" on the x-axis in such a
way that the x-axis goes through the center of the leaf (as if
it were a vein through the center of the leaf). We will call this
petal the "axis petal."

When k is even, there are 4 axis petals, each lying on the positive or negative side of the x- or y- axis.

Glance at the the graphs to verify these conclusions.
Then go on to "What
does **a** do?"