The Exploration says first I have to draw in the diagonals of the seven shapes, excluding the triangle, because triangles don't have diagonals. I connected the segments of each nonadjacent points for the seven shapes.
Then I entered the data into my graphing calculator. I placed the values, n, which is the number of sides, in List 1 (L1) and the corresponding values, d, which is the number of diagonals, in List 2 (L2).
Next I made a scatter plot of the data.
Then I used my calculator to figure out the linear regression, power regression, quadratic regression, cubic, and quartic regression.
I found out that the Quadratic Regression best fits the data. The equation is 0.5x^2 - 1.5x. The R^2, or correlation coefficient, is 1. The R^2 tells the strength and direction of the scatter plot. Since R^2 is positive 1, then the scatter plot has a positive association. Since all the data points fit exactly on the curve, then the strength is very strong, because 1 in correlation means that the scatter plot is very strong.
Finally, I used the Equation 0.5x^2 - 1.5x to find how many diagonals there are for a 200-gon. My calculations tell me that a 200-gon has 19700 diagonals.
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