SOLUTION: I need help with this problem. Please help me and show all work. Thanks A person standing close to the edge on top of a 144-foot building throws a ball vertically upward. The

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Question 1021026: I need help with this problem. Please help me and show all work. Thanks

A person standing close to the edge on top of a 144-foot building throws a ball vertically upward. The quadratic function h(t)=−16t^2+128t+144
h(t)=-16t^2+128t+144 models the ball's height about the ground, h(t)
in feet, t seconds after it was thrown.
a) What is the maximum height of the ball?
_________feet
b) How many seconds does it take until the ball hits the ground?
_________ seconds
Found 2 solutions by KMST, MathTherapy:
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
WITHOUT ALGEBRA 2:









a) From the last equation above we realize that
,
so the maximum height of the ball is feet.

b) The ball hits the ground when for a ,
so we need a positive solution for .
<--><-->--> .
<-->--> is the only option with ,
so the ball hits the ground seconds after it is thrown upwards.
WITH FORMULAS:
a) A quadratic function with
has a maximum for .

is such a function with , , and ,
so there is a maximum for
, and that maximum is
.

b) The ball hits the ground when for a .
So, we are looking for a positive solution to
<--><--><--> .

Since the solutions are and ,
the ball hits the ground seconds after it is thrown upwards.

The equation can be solved by factoring, by "completing the square", and by using the quadratic formula.
By factoring:

--->--->
By using the quadratic formula:
The quadratic formula says that any solution(s) for
, if there is any, are given by
,
so any solution(s) for ,
with , would be given by
--> .
Completing the square is pretty much what was done at the top:
<--><-->-->-->
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

I need help with this problem. Please help me and show all work. Thanks

A person standing close to the edge on top of a 144-foot building throws a ball vertically upward. The quadratic function h(t)=−16t^2+128t+144
h(t)=-16t^2+128t+144 models the ball's height about the ground, h(t)
in feet, t seconds after it was thrown.
a) What is the maximum height of the ball?
_________feet

b) How many seconds does it take until the ball hits the ground?
_________ seconds
Maximum height occurs at , or at , or at: 

Maximum height at  is: , or , or maximum height reached =  



Ball hits the ground when y, or height = 0, so we get:



 ---- Factoring out GCF, - 16

  

0 = (t - 9)(t + 1)

0 = t - 9        OR          0 = t + 1

t, or time it takes ball to hit the ground =             OR          - 1 = t (ignore)  

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