Write-up 12

by

Matt Sorrells

This assignment allows us to explore some aspects of spreadsheet programs. I chose to construct a graph of any function y = f(x) by generating a table of values with the x values in one column and the y values in another. The spreadsheet program that I used was Excel. I chose a random f(x). The function I chose first was f(x) = (x/2)^2. I chose to look at this function for x values ranging from -10 to 10. The x and y values are below.

 X Y1 -10 25 -9 20.25 -8 16 -7 12.25 -6 9 -5 6.25 -4 4 -3 2.25 -2 1 -1 0.25 0 0 1 0.25 2 1 3 2.25 4 4 5 6.25 6 9 7 12.25 8 16 9 20.25 10 25

Intuition told me that this should be a parabola and the x and y values seem to support this. The graph should tell us more.

The graph seems to further support the claim that this is a parabola, and indeed it is.

The second function that I looked at was -(x/2)^2+x-1. The x and y values are below.

 X Y2 -10 -36 -9 -30.25 -8 -25 -7 -20.25 -6 -16 -5 -12.25 -4 -9 -3 -6.25 -2 -4 -1 -2.25 0 -1 1 -0.25 2 0 3 -0.25 4 -1 5 -2.25 6 -4 7 -6.25 8 -9 9 -12.25 10 -16

This, too, should be a parabola. The graph is below.

Indeed, this is also a parabola.

The last thing that I did was put these x and y values together and graphed the functions together. Below are the x and y values.

 X Y1 Y2 -10 25 -36 -9 20.25 -30.25 -8 16 -25 -7 12.25 -20.25 -6 9 -16 -5 6.25 -12.25 -4 4 -9 -3 2.25 -6.25 -2 1 -4 -1 0.25 -2.25 0 0 -1 1 0.25 -0.25 2 1 0 3 2.25 -0.25 4 4 -1 5 6.25 -2.25 6 9 -4 7 12.25 -6.25 8 16 -9 9 20.25 -12.25 10 25 -16

And the two functions graphed together are below.