Question

A fireworks rocket is launched from a hill above a lake. The rocket will fall into the lake after exploding in the air. The rocket’s height above the surface of the lake is given by the function g(x)= -16x2 + 64x + 80 where x is the number of seconds after the rocket is launched. The function can also be written in factored form as g(x) = -16 (x + 1)(x - 5).When does the rocket hit the ground?

Answer 1

We are giving the function as;

$g(x)=-16x^2+64x+80$

If we factorize g(x) we have that

$g(x)=-16(x+1)(x-5)$

T0 find if the object has be launched and find the x value of the object

Therefore,

$\begin{gathered} -16(x+1)(x_{}-5)=0 \\ \Leftrightarrow(x+1)(x_{}-5)=0 \\ \leftrightarrow x=-1\text{ or x=5} \end{gathered}$

it will take the rocket 5 seconds to reach the ground.