Assignment 2:  Examining Graphs of Parabolas
By:
Jonathan Sabo

Examine graphs for the parabola

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

Try using the GC 3.5 animation by replacing a, b, or c with an n and selecting an appropriate range for n

First we graph the parabola where a, b, and c are all equal to 1.

We can see the vertex at (-1,1.5) and the graph has a line of symmetry at x = -1.  Lets observe what happens as we vary a, b, and c.

Observe as we vary a.

The first thing that I notice is the result from putting a negative sign in front of the function.  Everyting there is a negative sign in front the parabola is reflected.  The next thing that I notice is as |a| increases the parabola is being stretched vertically.  All of the graphs seem to be tangent to the line y = x + 1.

Observe as we vary b,

From this graph we notice that as b approaches -4 the graph will shift down and to the right.  We also notice that as b approaches +4 the graph will shift down and to the left.

Observe as we vary c,

From this graph we notice that as c decreases the graph will shift down and as c increases the graph will shift up.

What exactly is happening as we vary a,b, and c?

As B increases > 0
• The graph will move to the left
• The graph will move down
As B decreases < 0
• The graph will move to the right
• The graph will move down
As C increases > 0
• The graph will shift up by C.
As C decreases < 0
• The graph will shift down by C.
As A increases > 0
• The parabola will open upwards.
• The graph will continue to become more narrow.
As A decreases < 0
• The parabola will open downwards.
• The graph will continue to become more narrow.