**Kristin Ottofy**

Assignment 2

2. Fix the values for * a* and

Let a = 1 and b = 1. Here are the graphs for when c = -2, -1, 0, 1, and 2.

In this case, by varying c, we are translating the parabola vertically. This is seen in by looking at the y-intercepts, (0, 2), (0, 1), (0, 0), (0, -1), and (0, -2), respectively. Here, we can see that if a=b=1, then c is the y-intercept.

Looking at this graph where a=3 and b=-2, we can see that this conjecture holds.

Proof:

(x

^{2}+x+c) - (x^{2}+x+(c-1)) = c - (c-1) = 1

Thus, we are translating by the absolute difference between the two c values. The sign of the difference will tell the direction to translate.