If f(0) = 0.....then c = 0
And we have this system
a ( 1)^2 + b(1) = 2 ⇒ a + b = 2 ⇒ -2a - 2b = -4 (1)
a(2)^2 + b(2) = 9 ⇒ 4a +2b = 9 (2)
Add (1) and (2)
2a = 5
a = 5/2
b = 2 - a = 2 - (5/2) = -1/2
f(3) = (5/2)(3)^2 - (1/2)(3) =
45/2 - 3/2 =
42/2 =
21
