William Plummer - Assignment #2

Examine the following formula:

and its graph when **a** = 1 and **b** = 1

This is the same as the graph for the following equation:

where **c**=2.

What happens to this graph when the variable ‘**a**’ is varied?

Let’s set **a** equal to the following values:

The following graphs result:

When **a** = 0, the graph is a line that intersects the y axis at 2 and has a slope of 1.

This is consistent with plugging 0 in for **a**. The above equation becomes

Which equals

And since **b**=1 and **c**=2, the equation of the line becomes

As **a** increases in value, the line above changes into a parabola with the axis of symmetry as a negative x-value.

Further increases in the value of **a** result in the vertical stretching of the parabola and the vertex approaching the intersection with the y-axis

Let’s also look at what happens when a < 0. We will set a equal to the following values:

As **a** decreases in value from 0, the line changes into a parabola that opens down with the axis of symmetry as a positive x-value.

Further decreases in the value of **a** result in the vertical stretching of the parabola and the vertex approaching the intersection with the y-axis.

How does the change in **a** affect the shape of other graphs? Here are animations of variations in a for various graphs.