Question

Alicia watched a drone take off from a bridge. The height of the drone (in meters above the ground)minutes after takeoff is modeled byh(t) = −3+^2 + 12t +96Alicia 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 inthe equation.h(t) =2) How many minutes after takeoff does the drone land on the ground?

Answer 1

a.

Function:

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

Factoring -3, we have:

$\begin{gathered} h(t)=-3t^2+12t+96 \\ h(t)=-3(t^2-4t-32) \end{gathered}$

Middle term facotizing the term inside parenthesis:

$\begin{gathered} h(t)=-3(t^2-4t-32) \\ h(t)=-3(t-8)(t+4) \end{gathered}$

This is the factored form.

b.

h(t) is the height.

When it lands on the ground, the height (h(t)) is 0, so we have:

$\begin{gathered} h(t)=-3(t-8)(t+4) \\ 0=-3(t-8)(t+4) \end{gathered}$

If we solve this equation for t, we get the line drone lands on the ground.

Let's do this:

$\begin{gathered} -3(t-8)(t+4)=0 \\ t=8,-4 \end{gathered}$

Time can't be negative, so the solution is t = 8 seconds.