Question

The function f(x)=-2x^2+12x+32 models the approximate height of an object t seconds after it is launched. How many seconds does it take the object to hit the ground?

Answer 1

To find the ground-hitting point (the zeroes of the function), factor. 

$-2(x^2-6x-8)$
$2(x-4)(x-2)=0$
$x=4,x=2$

The ball will hit the ground 4 seconds after throwing.