Question

Tom started an entertainment company. The net value of the company (in thousands of dollars) ttt months after its creation is modeled by v(t)=4t^2-24t-28v(t)=4t 2 −24t−28v, left parenthesis, t, right parenthesis, equals, 4, t, squared, minus, 24, t, minus, 28 Tom wants to know when his company will be at its lowest net value. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation.

Answer 1

`v(t) = 4(t -7)(t +1)`

Explanation:

Given

`v(t) = 4t^2 - 24t - 28`

Required

Rewrite in a different form

To write in a factored form, we have:

`v(t) = 4t^2 - 24t - 28`

Expand

`v(t) = 4t^2 +4t- 28t - 28`

Factorize

`v(t) = 4t(t +1)- 28(t +1)`

Factor out t + 1

`v(t) = (4t -28)(t +1)`

Factorize 4t - 28

`v(t) = 4(t -7)(t +1)`