For assignment 2, you requested that we "explore ALL of assignment
2, then select one problem and prepare a write-up. I worked through all
the problems on 10/8 and have selected problem 8 to write-up.
Problem 8 asked me to produce 5 to 10 graphs of the form y = ( x - d )^
2 - 2. The graphs will appear below under a copy of the equations I graphed.
I did them all at once to expedite the completion of the assignment. From
past experience, I expected ,and got, a series of parabolas with vertex
at (d,-2). When explaining this to a class of students, I would do the graphs
one at a time and allow them to pick the values of d. As per question 5,
8 graphs appearing all at once would make little or no sense to students
studing parabolas. The exercise is meant to generate so insight into the
behavior of the parabolic function as d changes its value. Graphing all
of the graphs at once will not aid the students understanding in any reasonable
educational philosophy. The students need to see the different graphs taking
shape and moving with the changing values of d. A golden opportunity to
expand their mathematical reasoning processes would be lost by NOT doing
the graphs individually with discussion of what the students expected to
happen with each value change to d.
The equations that follow are the equations I used to generate the graphs.
The diagram below the equations is a copy of the graphs generated.
I realize that one of my graphs is not one of my functions. The errant
equation should be y = (x+3)^2 - 2 and not y = (x - 5)^2 - 2. I tried to
copy the equation the same day I made the copy of the graph, but experienced
technical difficulties and extreme patience stretching. Students should
extend this exercise as per the rest of assignment 2 and change the values
of c, to explore behavior of the function. For pratical purposes, x - (-1)
was written as x + 1. The same goes for x - (-2) and would have applied
to x - (-3) if I had made a correct copy on 10/8.