I set **b**=1 and **c**=0, which gave the equation y
= a sin x. I then tried different values for **a** and graphed
the results. Some examples follow.

It became clear that changing **a** caused changes in the
amplitude of the equation. In fact, the amplitude of the equation
is the absolute value of **a**. For positive values of **a**,
the graph simply stretched or shrank vertically. For negative
values of **a**, the graph was reflected about the x-axis and
also stretched or shrank vertically.

It is also important to note that changing **a** did not
affect the x-intercepts. The x-intercepts are the values of x
that will make y = 0. So for y = a sin x we have the following:

If a = 0, then the amplitude of the equation is 0 and we get the line y = 0.

If sin x = 0, then y = 0 regardless of the value of **a**.

The x-intercepts remain the same for all values of **a**
except 0.

Click **here** to see
an animated graph of this equation.