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
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 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
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
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.