Correlation Between Rectangle Grids and Difference Patterns

math1234225r4422

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Jun 23, 2016
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Hello,

I am doing a math investigation for school and I have to find the correlation between two difference patterns and rectangle grids. The investigation starts by showing y values when x is 0, 1, 2, 3, 4 and 5 for the equation 2x^2 + 3x +1. The answers show;
x 0 1 2 3 4 5
y 1 6 15 28 45 66.
Then it goes on to show the difference between the y values that are given from increasing consecutive x values, e.g
6-1=5
15-6=9
28-15=13
45-28=17
66-45=21.
Then it shows the difference of all those (9-5, 13-9, 17-13, 21-17) which all become 4. It tells us that we now no longer need to find the third, fourth, ect. differences because they would all equal 0.
It asks us to complete the table for the rule y=ax^2 +bx+c and the answers show;
x 0 1 2 3
y c a+b+c 4a+2b+c 9a+3b+c
first difference a+b 3a+b 5a+b
second difference 2a 2a

Then the second part of the investigation shows a rectangular grid, and we have to find how many rectangles (squares included) can fit on the grid. The formula x(x=1)*y(y+1)/4 is given, where x is length and y is width.
eg. 1*3 rectangular grid, sub in values so 1(1+1)*3(3+1)/4 gives 6 possible rectangles.

My question is, what is the correlation between the two and how do they relate (it may have something to do with difference of perfect squares or triangular numbers?)

Regards,

Thank You.
 
...what is the correlation between the two and how do they relate (it may have something to do with difference of perfect squares or triangular numbers?)
I think the point of the exercise is that you're supposed to think about this, and come up with something of your own. So: What are your thoughts? What have you tried? Where are you stuck?

Please be complete. Thank you! ;)
 
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