Make the following observations about the graphs
of the equation when **k** is odd and the go on to investigate
graphs of this equation when "**k** is even."

Since **k** is odd, there are **k** petals
with a petal lying on the y-axis. Review
when this axis petal lies on the positive or negative y-axis.
We can classify the graphs into three groups:

1.

Single roseswith closed petals that converge at the origin. This occurs when b = 0 and whenb = 2a.The radius of the rose is given byr = 2a + b.(graphs in

blackandgreen).2.

Double rosescomposed of outer and inner petals. This occurs whenb < 2a. There are two radii to consider: the radius of the (1) outer rose is given byr = 2a + b.(2) the inner rose is given byr = 2a - b.(graphs in

purple,red, andblue)3.

Open-petaled roseswith an opening or core in the center. This occurs whenb > 2a. There are two radii to consider: the radius of the (1) rose is given byr = 2a + b.(2) the core is given byr = 2a - b.(graphs in

cyanandyellow)

** NOTE:**
The graphs of the equations with negative values of

Also, recall
that if **a** or **k** (but not both) is **negative**,
the graph is reflected about the x-axis. If **BOTH** **a**
and **k** are negative, then the graph is the same as if both
were positive.