(1, 50)

(2, 150)

(3, 300)

(4, 500)

(5, 750)

(6, 1050)

If (x, y)

what is the formula to find much higher x values?

Guest Aug 18, 2015

#6**+5 **

Miss Melody, I look and see if maybe can I do it .

I need practice in my writing so it will help for that too.

Also if I make a mistake I can fix it if you tell me.

Dragonlance
Aug 19, 2015

#3**+7 **

If you subtract successive y-terms (bottom up so that they are all positive):

150 - 50 = 100 300 - 150 = 150 500 - 300 = 200 750 - 500 = 250 1050 - 750 = 300

If these answers were all the same number, your formula would be a linear equation: y = ax + b, but since they aren't, subtract the answers (again, subtract smaller from larger):

150 - 100 = 50 200 - 150 = 50 250 - 150 = 50 300 - 250 = 50

Since these answers are all the same and since it took two sets of subtractions, the formula will be quadratic: ax^{2} + bx + c = y

(1,50) --> x = 1, y = 50 --> a(1)^{2} + b(1) + c = 50 --> a + b + c = 50

(2,150) --> x = 2, y = 150 --> a(2)^{2} + b(2) + c = 150 --> 4a + 2b + c = 150

(3,300) --> x = 3, y = 300 --> a(3)^{2} + b(3) + c = 300 --> 9a + 3b + c = 300

Now solve these for a, b, and c:

Combining the first two: a + b + c = 50

4a + 2b + c = 150

Subtracting: 3a + b = 100 (subtract bottom up)

Combining the last two: 4a + 2b + c = 150

9a + 3b + c = 300

Subtracting: 5a + b = 150 (subtract bottom up)

Combining these two answers:

3a + b = 100

5a + b = 150

Subtracting: 2a = 50 ===> a = 25

Substituting back: 5(25) + b = 150 ---> b = 25

and finally, a + b + c = 50 ---> 25 + 25 + c = 50 ===> c = 0

So, the equation is: ax^{2} + bx + c = y ===> y = 25x^{2} + 25x

geno3141
Aug 18, 2015

#5**+1 **

**Yes thank you Geno.** I would not have known how to do it either.

I might have muffled through to an answer but it would not have been well organised like yours is.

Thank you also Dragonlance for bringing Geno's answer to my attention!

I have put this in our "Reference material" sticky topic threads

**That Reference thread really needs to be reorganised - any volunteers ? :))**

Melody
Aug 19, 2015

#6**+5 **

Best Answer

Miss Melody, I look and see if maybe can I do it .

I need practice in my writing so it will help for that too.

Also if I make a mistake I can fix it if you tell me.

Dragonlance
Aug 19, 2015