Assignment 2: Let's C Where This Will Go

By Kendyl Wade

For this exploration, we will take the quadratic formula:

and keep a and b the same while varying c.

From what I know about functions, changing c should shift the function up and down, but let's double check!

Here we will let a = 1, b = 1, and let c be integers from -2 to 3.

Notice that the y-intercept of each function is the value of c. Now let's see an animation of the function while c changes.

It appears that indeed the function is shifting up and down! But how do we prove this?

Observe as we take the quadratic equation and get it in vertex form:

Here we can see that regardless of what c is, the x-coordinate of the vertex will always be -1/2. So the only thing that changes about the shape and position of the vertex is the y-coordinate of the vertex.