discovering quadratics

Question

A projectile is fired vertically upward and can be modeled by the function h(t)=−16t^2+900t+150t. During what time interval will the projectile be more than 8000 feet above the ground? Round your answer to the nearest hundredth.

Answer 1

16t^2 -1050t +8000=0

8t^2-525t +4000= 0

graph it, x = about 9 and 57

57-9=48 seconds above 8,000 feet

use the quadratic formula

x=525+/- 5sqr5905]/16= about 56.826 and (525-5sqr5905)/16=8.7988

56.826-8.799= 48.27= about 48 1/4 seconds

the interval (8.80, 56.83)