Posted by **Cassidy** on Friday, June 5, 2009 at 9:32am.

I'm having a hard time figuring out a quadratic model for this data.

x y

----------

1 3

2 13

3 31

4 57

5 91

6 133

How do I go about doing this?

Is there a website that could help me?

- Algebra II -
**MathMate**, Friday, June 5, 2009 at 10:00am
First show that this is a quadratic relationship by taking differences and second differences:

y dy d^{2}y

3 10 8

13 18 8

31 26 8

57 34 8

91 42 8

133

If the second difference is constant, it is a quadratic relationship.

Assume the quadratic model as:

f(x)=ax^{2} + bx + c

then

f(x+1)=a(x+1)^2+b(x+1)+c

and

f(x+1)-f(x)=2ax+b+a

Similarly,

f(x+2)-f(x+1)=2ax+b+3a

f(x+3)-f(x+2)=2ax+b+5a

....

Thus, the second difference = 2a

2a=8

a=4

By substituting values of x and a into one of the formulas, b can be found

for x=1,

dx=10

2ax+b+a=10

b=-2

Substitute a and b in f(1), we get

2(1)^{2}-2(1)+c=3

c=1

Thus

f(x)=4x^{2}-2x+1

check:

f(1)=3

f(3)=31

f(6)=133

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