Assignment #2:

Exploring the Parabolas

In this assignment, we will be constructing graphs of the parabola

y = ax2 + bx + c

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

How does a change the parabola?

In the following graph, we are going to hold b and c constant and vary a.

*Notice:

When a is positive, the parabola opens upward (concave up).

When a is negative, the parabola opens downward (concave down).

As the value of a gets bigger, the more narrow the parabola becomes.

As the value of a gets smaller, the more wide the parabola becomes.

How does b change the parabola?

In the following graph, we are going to hold a and c constant and vary b.

*Notice:

The graph of   is centered on the xy-plane and is one unit up from the origin.

As b increases positively, the parabola dips lower and lower to the left.

As b decreases negatively, it dips lower to the right.

How does c change the parabola?

In the following graph, we are going to hold a and b constant and vary c.

*Notice:

As the values of c increase, the parabola becomes more narrow and the vertex increases.  Similarly, as c decreases, the parabola becomes more wide and the vertex decreases.