The quadratic function h (t)=-16t^2+150 models a balls height, in feet, over time, in seconds, after it is dropped from a 15 story building. from what height in feet was the ball dropped? after how many seconds did it hit the ground?

Hello! Lets solve this :)
So for the first question :
h(t) = -16t^2 + 150
h(0)= -16 (0)^2 + 150
h(0)= -16(0) + 150
h(0)= 0 + 150
h(0)= 150 feet

Second question
We need to find here the time when the ball hit the ground; or when the height h(t) is 0.
In equation form
h(t) --> 0=16t^2 + 150
16t^2 = 150
t^2=150/16
t= √150/16
t= 5√6/4
t= 5 (2.45)/4
t= 3.06 seconds

Hope this helps! If you have any other questions or would like further explanation just let me know! :)