Question

a ball thrown from the top row of seats. the function h(t)=16t^2+80t+96 give the hight in feet, of the ball t seconds after it is thrown. how long does it take before the ball hits the ground?

Answer 1

When h(t)=0 the ball reaches the ground, so 16(t²+5t+6)=0, so t²+5t+6=0=(t+3)(t+2)  which gives us negative values for t, so I suspect that 16t² should be -16t².

So we would have -t²+5t+6=0, that is, t²-5t-6=0=(t-6)(t+1) and t=6 seconds is the time the ball takes to reach the ground. We ignore t=-1 as meaningless (time before the ball was thrown).

The constant 96 feet is the height of the top row of seats. -16t² is the negative effect of gravity on the ball and  80 feet per second is the vertical component of the speed the ball was thrown. This is how h(t) was constructed.