The function is given to be:
[tex]-2x^2-8x+42[/tex]
The object hits the ground when the function is equal to zero:
[tex]-2x^2-8x+42=0[/tex]
Solving the equation by factorization, we have:
[tex]\begin{gathered} 2(-x^2-4x+21)=0 \\ -x^2-4x+21=0 \\ -x^2-7x+3x+21=0 \\ -x(x+7)+3(x+7)=0 \\ \therefore \\ (-x+3)(x+7)=0 \\ Hence \\ x=3,x=-7 \end{gathered}[/tex]
Since the time cannot be negative, then the time will be 3 seconds.
Therefore, it will take 3 seconds for the object to hit the ground.
