"A quadratic function f contains these points.

x y

3 36.7

5 27.5

7 20.7

9 16.3

11 14.3

Find the particular equation for f(x) as a function of x."

Here is my response:

ax^2+bx+c

36.7=a(3)^2+b(3)+c

36.7=9a+3b+c

36.7-9a-3b=c

27.5=a(5)^2+b(5)+(36.7-9a-3b)

-9.2=16a+2b

(-9.2-16a)/2=b

20.7=a(7)^2+((-9.2-16a)/2)7+(36.7-9a-3((-9.2-16a)/2))

20.7=49a+(-4.6-8a)7+(6.7-9a-3(-4.6-8a))

20.7=49a-32.2-56a+6.7-9a+13.8+24a

20.7=-11.7+8a

32.4=8a

a=4.05

16.3=4.05(9)^2+((-9.2-16(4.05))/2)(9)+(36.7-9(4.05)-3((-9.2-

16(4.05))/2))

16.3=4.05(9)^2-37(9)+111.25

Unfortunately, after double checking it into the calculator (using quadratic regression), the real equation is $\displaystyle 0.3x^2+-7x+55$ ...I'm at a bit of a loss.

Any help would be greatly appreciated