Assignment 2: Construct graphs for the parabola

for different values of a, b, and c. (a, b, c, can be any rational number).

To begin this investitgation, I will set b=1 and c=1. I will be exploring the different graphs as the (a) value varies .

Make at least 5 graphs on the same axes as you vary (a) value.

Clearly when a=1 we have . This equation is represented by the red parabola in the graph below.

Now, look at the graphs for a=-4, -3, -2, -1, 0, 1, 2, 3, 4. The nine graphs are on the same axes. Notice if a=0 we have a linear equation. The nine graphs meet at the point x=1. This is due to the constant in the above equation.

Now, I will set a=1 and b=1. I will be exploring the different graphs as the (c) value varies.

Notice, for this eqation if c=1, the the graph of the equation is same as the red parabola above. Look at the graphs for c=-4, -2, 0, 2, 4. The five graphs are on the same axes.

Notice that for c=0, the graph of passes through the orgin. There seems to be downward shifts as c decreases.