#### How does the value of a affect the graph?

**What affect does a positive value of a have
on the graph?**

Before, when a =1, each of the graphs went
through the origin.

When a = 2, the graph no longer goes through
the origin.

Below is a layered graph, showing when a=3,
4, 5, and 6.

**What effect will a < 1 have on the graph?**

From this layered graph we can draw several
conclusions

A value of a that is a fraction less than 1
will

* have the same general shape as the typical
"n leaf" rose.

* have 2 sets of petals.

* have outer petals that are shorter than those
of a related graph

* have inner petals that are longer than those
of a related graph

From this layered graph, we can see that the
larger the denominator of a gets, the closer the outer and inner
petals get to each other.

**What happens when a is negative?**

Nothing. The graph remains the same.

Click **here**
to see a discussion of the graph when a = 0.

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to return to the Polar Equations main page.

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