(2,14),(1,-1),(3,35)
Find the quadratic function y=ax^2+bx+c
1) 4a+2b+c=14
2) a+b+c=-1
3) 9a+3b+c= 35
equation 1&2 = 3a + b = 13
equation 1&3 = -5a +5b = -21
It is easier if you write y as:
y = A (x-1)(x-3) + B(x-2)(x-3) +
C(x-2)(x-1)
y(1) = -1 ---->
2 B = -1 --->
B = -1/2
y(2) = 14 ------->
A = -14
y(3) = 35 --------->
C = 35/2
So, we have:
y = -14(x-1)(x-3) -1/2 (x-2)(x-3) +
35/2 (x-2)(x-1) =
3 x^2 + 6 x -10