EMAT 6680
Transformers! Parabolas in Disguise!
By Stephanie Britt
Transformations of Parabolas is a subject that is difficult for many students to understand. When we change the way the equation looks shouldn't it change the way the graph looks? Unfortunately many students do not make the connection of how or why the graph looks similar to the parent graph, but has only shifted left, right, up or down. This assignment shows how simple it can be.
The graph of this parent function looks like:
The vertex is at (-0.75, -5.125)
Now if we replace x with (x-4) in the equation we get a change. Can you notice the shift?
So the new graph looks like:
With the new vertex at (3.25, -5.125)
So the vertex moved in a positive direction on the x-axis four units, but not up or down on the y-axis.
If we add 7 positive units to the original parent function what will happen?
The graph looks like:
We can see the vertex shifted to (-.75, 1.875) or up 7 units on the y-axis from the parent graph.
Are we starting to notice a pattern?
What is it going to take to make the parent function flip upside down? It is not just as simple as changing the sign of the first term. One must know how to complete the square of the equation which is also known as vertex form. Through a complicated process the new formula for the reflected equation is:
or
With the graph being successfully refleted.
If you notice the vertex of the parent function is 1.125 units away from the y-intercept. With the new equation the vertex is also 1.125 units away from the y-intercept, It is just in the opposite direction.