Question

The function -2x^2-8x+42 represents the approximate height of an object (x seconds) after it is thrown off the top of a building. How many seconds does it take for the object to hit the ground?

Answer 1

The function is given to be:

$-2x^2-8x+42$

The object hits the ground when the function is equal to zero:

$-2x^2-8x+42=0$

Solving the equation by factorization, we have:

$\begin{gathered} 2(-x^2-4x+21)=0 \\ -x^2-4x+21=0 \\ -x^2-7x+3x+21=0 \\ -x(x+7)+3(x+7)=0 \\ \therefore \\ (-x+3)(x+7)=0 \\ Hence \\ x=3,x=-7 \end{gathered}$

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.