Assignment Two

Charles Meyer



I have decided to investigate a very common equation as part of assignment two. I chose this equation due to its frequent use in middle school algebra classes. While most young people soon realize that the graph of this equation produces a parabola, it is not easily seen what happens as the value of a changes.


I will begin by looking at a graph of the equation with a=1.

This equation of course produces a parabola in the positive direction. A negative coeffiecent produces just the opposite.


The question though to middle schoolers should be, what happens when the value of a is changed? We can investigate this through the use of the graphing calculator software which provides us a way to overlay a series of equations on the same set of axis and helps demonstrate the changes that are occuring. I will start by taking values of a and increasing them by 1.

It should be seen that as the value of the coeffecient increased, the parabola "closed up". In other words, the distance between the positive and negative y values became less and less at corresponding x values. At very large coeffecient values, the parabola would almost seem to touch the y axis and give the illusion of a single vertical line. Of course the values of our coeffecient a can become very small as well.


Once again we can see the changes that are occuring in our graph. As the values of a become smaller, the parabola "opens up" and spreads out away from the y-axis. If a were assigned a very small number, the graph would begin to resemble a horizontal line along the x-axis.


Middle school and freshmen algebra students should take note the power of the coefficeint. A change in the coeffeicent can and will greatly change the look and function of the equation.


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