# 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.

###

###

###