Assignment 3

Assignment 3

Johnie Forsythe

Let's explore the equation

To begin our exploration, we will consider different values of a, b, or c as the other two are held constant.

Lets begin by exploring the variable a.

If we set

for a = -3, -2, -1, 0, 1, 2, 3, and overlay the graphs, the following picture is obtained.

NOTE: The colored boxes correspond with the colored parabolas

Observations:

- The parabola always passes through the same point on the y-axis (point (0,1)).

- The vertex of the parabola changes in each equation.

- The concavity of the parabola changes in each equation.

Let's now set

for b = -3, -2, -1, 0, 1, 2, 3, and overlay the graphs. The following picture is obtained:

Observations:

- Again, the parabola always passes through the same point on the y-axis (point (0,1)).

- Again, the vertex of the parabola changes in each equation.

- However, the concavity of each parabola seems to have stayed consistently the same.

FInally, let's set

for c = -3, -2, -1, 0, 1, 2, 3, and overlay the graphs. The following is obtained:

Observations:

-The parabola does NOT pass through the same point as c changes.

- The vertex of the parabola changes in each equation.

- The concavity of the parabola increases as c increases.