Find a quadratic model for the sequence y0505x4 y 05x2153 y

Find a quadratic model for the sequence. y-0.5%-0.5x-4 y = 0.5x2-1.5-3 y 4.5x2-21.5x+21 y =-4.5x2 + 21.4x-21

1) Quadratic model for the sequnce:

x = 0 y =-4

x=1 ; y =-4

x=2 ; y =-3

x=3 ; y = -1

y = ax^2 +bx +c

Plug these values to form equations to solve a, b, c:

-4 = c

Now we have the equations with constnat term = -4 as Option 1

y = 0.5x^2 -0.5x - 4

Lets verify one points i.e. x= 3 ; y =-1

-1 = 0.5(3)^2 -0.5(3) -4 It satisfies

So, option A

2) first diffenerces ------ second differences

a1 -1

a2 1 --------( 2)

a3 -1 ---------- (2) ----------------------------- (0)

a4 5 ---------( 6) ------------------------------(4)

a5 15 ------- ( 10) ---------------------------(4)

Since the second differences are not equal sequnce is not quadratice

So, Option : first differenec : 2, 2 , 6 , 10 not quadratic