The speed of a firework x seconds after lighting up can be modeled with the expression -x2 + 4x + 32. How long after lighting the firework does the firework stop moving?

Question

The speed of a firework x seconds after lighting up can be modeled with the expression -x² + 4x + 32. How long after lighting the firework does the firework stop moving?

Answer 1

 -x² + 4x + 32

Factor out -1

-(x²-4x-32)=0

Factor

-(X-8)(x+4)=0

Set each equal to zero

x-8=0. X=8

If you set x+4=0 you get x=-4 which we can disregard since we cannot have negative time

So the answer is 8 seconds