In this investigation, we will try to figure out the number of different half time scores for when you only know the total number of goals scored for the game.
First, let’s list down all the possible halftime scores for total number of goal scored in the entire game.
Let T = total number of goals scored in the entire game.
H = Possible half time scores
First, let’s list down all the possible halftime scores for total number of goal scored in the entire game.
Let T = total number of goals scored in the entire game.
H = Possible half time scores
From this diagram 1, I noticed that the first difference goes up in a pattern of 3, 6, 10, 15, and so on. However the second difference is a constant of 1. This means that this is a quadratic number pattern with a general formula:
To find the value of a, the rule is the half of the second difference.
a = ½(second difference)
= ½ (1)
a = 0.5
To find the value of c, the rule is the value of y when x=0. Looking at diagram 2, y = 1 when x = 0 (0-0)
c = 1
The equation right now is:
a = ½(second difference)
= ½ (1)
a = 0.5
To find the value of c, the rule is the value of y when x=0. Looking at diagram 2, y = 1 when x = 0 (0-0)
c = 1
The equation right now is:
Finally, to ensure that the formula is correct, I tried two examples and compared it to table 2.
Conclusion: If the total number of goals scored in the entire game is given, you can find the number of possible half-time scores by using the equation