Assignment Two
by
Rachael Brown
The Problem: Examine the graphs of quadratics
in standard form by keeping 2 values fixed and varying one value.
My first step was to use graphing calculator
and fix a and b while varying c. Here is the graph that I obtained:
As you can see, it looks like varying
c shifts the parabola up or down. It looks like adding a number
raises the graph and subtracting a number lowers it. It looks
like a vertical translation. It does not look like the location
of the parabola and the value of c relate simply. For example,
when c is 3 I don't know how that relates to the grey parabola.
Next, let's see what happens when we
fix a and c and vary b. Here is the graph that I created:
From the graphs and equations we can
see that b seems to cause a horizontal shift in the parabola.
For example, focus on the gray and purple parabolas. They appear
to be mirror images of each other about the y-axis. The only thing
that seems to change about the gray parabola compared to the purple
parabola is a shift to the left. The vertices of all the parabolas
seem to connect to the value of b. It looks like vertex's x-coordinate
is the opposite of b.
Finally, let's look at what happens
to the graph of the parabola as we vary a and keep b and c as
constants.
This is very different from what we've seen
before. The a value seems to control whether the parabola opens
up or down. The blue, red, and purple parabolas open down and
the a values for all three were negative. Thus, a negative a value
must make the parabola open down. We also see the vertex seems
to be moving even though c and b are constant. It appears as though
a has a more complicated control over the parabola. I did not
include when a = 0 in my list. What do you think it would look
like?
Let's see...
Is it what you expected? Without the
x-squared term we have a line. This line is what separates the
negative and positive values.
Now we seem better prepared to guess
and check the equation of a parabola. See if you can find the
equation for the parabola below.
Click on the graph to open this in
Graphing Calculator to see if you are right.
Back.