An object is thrown upward at a speed of 152 feet per second by a machine from a height of 9 feet off the ground. the height h of the object after t seconds can be found using the equation h=−16t^2+152t+9
when will the height be 231 feet?
when will the object reach the ground?

First part:

Set h(t) = 231and solve for t.

-16t²+ 152t + 9= 231

-16t² + 152t - 222= 0

Solve this quadratic equation for t. You should get 2 positive solutions. The lower value is the time to reach 231 on the way up, and the higher value is the time to reach 231 again, on the way down.

Second part:

Set h(t) = 0 and solve the resulting quadratic equation for t. You should get a negative solution (which you can discard), and a positive solution. The latter is your answer.