Decide which of the two given functions is linear and find i

Decide which of the two given functions is linear and find its equation.

Solution

g(x) is linear

let g(x) = ax^2 + bx +c ( normally we don\'t know yet that g(x) is linear )

(0,-1) (3,5) (6,11) are poins

g(0) = 0 + 0 +c

-1 =c

so c = -1

g(3) = 9a +3b -1

5 = 9a +3b -1

9a +3b =6 ------>1

(6,11) plug

g(6) =36a +6b -1

11 =36a +6b -1

36a +6b =12 ------->2

solving 1 and 2 we get a =0 and b=2

so g(x) = 0x^2 +2x -1

g(x) = 2x -1

so finally g(x) = 2x -1 and it is linear