Alicia watched a drone take off from a bridge. The height of the drone (in meters above the ground) minutes after takeoff is modeled by h(t)=−3t2+12t+96h(t)=-3t^2+12t+96h( t)=−3t2+12t+96h, left parenthesis, t, right parenthesis, equals, minus, 3, t, squared, plus, 12, t, plus, 96 Alicia wants to know when the drone will land on the ground. 1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation. h(t)=h(t)=h(t)=h, left parenthesis, t, right parenthesis, equals 2) How many minutes after takeoff does the drone land on the ground?

Step-by-step explanation:

Given the height of the drone modelled by the equation:

h(t)=-3t^2+12t+96

a) Rewriting this in a factored form.

From the equation, we can see that -3 is the greatest common factor. The equation therefore becomes:

h(t)= -3(t^2-4t-32)

Hence the function can also be written as h(t)= -3(t^2-4t-32)

b) The drone landed on the ground at when h(t) = 0. Substitute h(t) = 0 into the expression  h(t)= -3(t^2-4t-32)

0 = -3(t^2-4t-32)

Divide through by -3

(t^2-4t-32) = 0

Factorize

t²+8t-4t-32 = 0

t(t+8)-4(t+8) = 0

(t-4)(t+8) = 0

t-4 = 0 and t+8 = 0

t = 4 and t = -8

Time can't be negative:

t = 4minutes

Hence it took the drone 4 minutes take off to land on the ground

after simplifying it i got: -36.25 as my answer. hope that !