Polynomial function: d=0.5n^2-1.5n Number of diagonals in a decagon: 35
Practice makes perfect
Since the data is equally-spaced, investigating the difference sequences will help us find the degree of the polynomial function that describes the data.
The second difference sequence is constant, so the polynomial describing the data is quadratic.
This function can be found algebraically, or we can use a calculator to find the quadratic regression function.
Push the STAT button, choose Edit, and enter your values.
To access the option for quadratic regressions, press the STAT button and choose QuadReg from the CALC menu.
After matching the lists for the x- and y-values, move to the last line and press ENTER.
The result screen gives the coefficients of the quadratic model.
Do not forget to change the variables from x and y (which the calculator uses) to n and d used in the context of this question.
d= an^2+ bn+ c
⇓
d= 0.5n^2 -1.5n
We found that the number of diagonals in a polygon with n sides is d=0.5n^2-1.5n.
Let's apply this formula for n=10 to find the number of diagonals in a decagon.
