Rewrite the equation in vertex form by completing the square

f(x)=(3x-9)(x+1)

f(x) = 3(x - 1)² - 12

Step-by-step explanation:

Given

f(x) = (3x - 9)(x + 1) ← expand factors using FOIL

     = 3x² - 6x - 9

To complete the square the coefficient of the x² term must be 1

Factor 3 out of 3x² - 6x

f(x) = 3(x² - 2x) - 9

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 2x

f(x) = 3(x² + 2(- 1)x + 1 - 1) - 9

     = 3(x - 1)² - 3 - 9

     = 3(x - 1)² - 12 ← equation in vertex form

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

b

step-by-step explanation: