The function h (t) = - 16t^2 + 16t + 32 models the height of a ball t seconds after it was thrown into the air. How long does it take for the ball to hit the ground?

When the ball hits the ground, h will be 0 so set up the equation

-16t^2+16t+32=0

divide all by - 16 to simply the equation

t^2-t-2=0

(t-2) (t+1) = 0

t=2 t=-1

you can't have - 1 second

so the answer is it takes 2 seconds for the ball to hit the ground