SOLUTION: I need help on what the steps are to solve this quadratic problem. Please show the problem with steps included. Thank you :) Imagine yourself standing on the roof of a 1450-foot

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Question 978501: I need help on what the steps are to solve this quadratic problem. Please show the problem with steps included. Thank you :)
Imagine yourself standing on the roof of a 1450-foot Tower. When you throw a ball upward from the roof of the tower, the ball’s height above the ground, H (in feet), can be described as a function of the time, t (in seconds), since the ball was dropped. This height function is defined by
H(t) = -16t2 + 80t +1450
Identify the vertical intercept and what does it mean in the context of the problem
After the baseball is thrown, how long will it take till the ball hits the ground?

Your answer to question #2 identifies one horizontal intercept of the equation. Identify another horizontal intercept and discuss whether it makes sense in the context of the problem.
At what time(s) is the ball 1500 feet above the ground?
Identify the practical domain and range.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The ball is not dropped. The ball must be thrown UPWARD. Note the -16 coefficient on x^2. H is concave downward and H has a vertex at a maximum.

Here is a way, not the only, to find vertex.
Roots...
H=0,
t=%28-80%2B-+sqrt%2880%5E2-4%28-16%291450%29%29%2F2%28-16%29

t=%28-80%2B-+sqrt%2815360%29%29%2F%28-32%29

15360=6*256=6*4*64=2*3*2*2*2^6=2^9*3

t=%28-80%2B-+16sqrt%286%29%29%2F%28-32%29

t=%2880%2B-+16%2Asqrt%286%29%29%2F32




t=40%2F16%2B-+%281%2F2%29sqrt%286%29

t at the vertex will be 40%2F16=20%2F8=10%2F4=5%2F2 which is exactly in the middle of the two roots. That is two and one-half seconds. Use this value of t=5/2 to find H%282.5%29. That is maximum value, the vertex of H.