Aperson sitting in the top row of the bleachers at a sporting event drops a pair of sunglasses from a height of 24 feet. the function h=−16x2+24h=−16x2+24 represents the height hh (in feet) of the sunglasses after xx seconds. how long does it take the sunglasses to hit the ground, rounded to the nearest tenth?

This graph is a negative parabola.  The ground is at a height of 0, so set h=0 and solve for x.
0 = -16x²+24
16x² = 24
x² = 24/16 = 1.5
x = +/-√1.5  ≈ +/- 1.2
Since x represents time, the negative answer is not valid (unless you have a time machine and can go backwards in time).
So, it takes ≈ 1.2 seconds for the sunglasses to hit the ground.