Answer:
1 and 37/8 feet
Step-by-step explanation:
We set h(t) to 76 because we want to know when the ball will be at 76 feet high.
So, we have 76=-16t^2+90t+2. When we subtract 76 from both sides, we get -16t^2+90t-74=0, and when you mutiply the equation by -1 (so that x^2 has a positive coefficient, which makes things easier), we get 16t^2-90t+74=0.
We notice that each separate monomial has a common factor, 2, so we can take that out and make it 2(8t^2-45t+37) = 0. Factoring the quantity in the parentheses gives us 2(t-1)(8t-37) = 0.
Using Zero Product Property, we can set the two factors in parentheses to 0 (the 2 isn't really relevant so we don't need to worry about it). This gives us t-1=0 and 8t-37=0. Solving these two equations gives us t = 1 foot or t = 37/8 feet.
