Ch. 1: Modeling with Functions and Regression Equations -- Option 2: Exploration, Diagonals of a Regular Polygon p. 158

(Click on the image[s] below to see them more clearly!)
1) First, I drew 8 polygons consisting of 3-10 sides. Then, I drew in all the possible diagonals for each of those polygons and recorded the number of diagonals present corresponding to the number of sides.

2) Second, I created a scatter plot with the number of sides on the X-axis and the number of diagonals on the Y-axis.

3) Third, I used my graphing calculator to figure out which curve fits best to the data, and recorded the value of r for each type.

4) After doing this, I found out that the quadratic regression fits perfectly. If you look closely (or click on the image to zoom), the equation would've been y=0.5x²-1.5x+0.

5) I then realized and explained that the cubic and quartic regressions could be predicted, since it would be the same if it was a quadratic regression. More details are within the second image.

6) Lastly, since I had to find the number of diagonals in a 175-gon, I plugged in 175 into x in the equation y=0.5x²-1.5x. After doing this, I know now that 15,050 diagonals are in a 175-gon.