Golfer hits the ball. the quadratic function y= -16x^2+80x gives the time x seconds when the golf ball is at height 0 ft. how long does it take for the golf ball to return to the ground?

You factorize, and solve for $y = 0$
$y = - 16 {x}^{2} + 80 x = - 16 \cdot x \cdot \left(x - 5\right) = 0 \to$
So $x = 0 \mathmr{and} \left(x - 5\right) = 0 \to x = 5$ seconds