Question

The height of a rocket x seconds after it is launched from a hill that is 224 feet high is modeled by the function f (x) = -16x² + 80x + 224.

How long does it take the rocket to hit the ground?
It takes (?) seconds.​
need asap thank you

Answer 1

t = 7 seconds

Explanation:

The height of a rocket x seconds after it is launched from a hill that is 224 feet high is modeled by the function :

f (x) = -16x² + 80x + 224

We need to find how long does it take the rocket to hit the ground. At that point,

f(x) = 0

`-16x^2 + 80x + 224=0\\\\(-16x^2)/(16)+(80x)/(16)+(224)/(16)=0\\\\-x^2+5x+14=0\\\\-x^2+(7-2)x+14=0\\\\-x^2+7x-2x+14=0\\\\x(-x+7)+2(-x+7)=0\\\\(x+2)(-x+7)=0\\\\x=-2\ \text{and}\ x=7`

Neglecting -2. Hence, the rocket will take 7 seconds to hit the ground.