How do I find the quadratic regression curve

Question

How do I find the quadratic regression curve through the given points :

(2,0) (-3,5) (-4,3)

thanks very much

Answer 1

not much choice here.......

y = Ax^2 + Bx + C

(2,0) ---> 0 = 4A + 2B + C

(-3,5) ---> 5 = 9A - 3B + C

(-4,3) ---> 3 = 16A - 4B + C

subtracts Equation 2 - Equation 1:

5 = 5A - 5B

1 = A - B <--- call this equation ALPHA

subtracts Equation 3 - Equation 2:

-2 = 7A - B <---- call this equation BETA

subtracts equation ALPHA - BETA:

3 = -6A

A = -1/2

equation ALPHA forces B = -3/2

original first equations says:

0 = 4(-1/2) + 2(-3/2) + C

0 = -2 + -3 + C

0 = C + -5

C = 5

the parabola is y = (-1/2)x^2 + (-3/2)x + 5

x=2 ---> (-1/2)(2)^2 + (-3/2)(2) + 5 = (-1/2)*4 + (-3/2)*2 + 5 = -2 + -3 + 5 = 0

x=-3 ---> (-1/2)((-3)^2) + (-3/2)(-3) + 5 = (-1/2)(9) + (-3/2)(-3) + 5 = -9/2 + 9/2 + 5 = 5

x = -4 ---> (-1/2)((-4)^2) + (-3/2)(-4) + 5 = (-1/2)(16) + (-3/2)(-4) + 5 = -8 + 6 + 5 = 3

the parabola is y = (-1/2)x^2 + (-3/2)x + 5