SOLUTION: A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by h(t) = −4.9t2 + 18t + 8. How long d

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Question 1153181: A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by
h(t) = −4.9t2 + 18t + 8.
How long does it take to reach maximum height? (Round your answer to three decimal places.)
Found 3 solutions by ikleyn, Edwin McCravy, MathLover1:
Answer by ikleyn(52915)   (Show Source): You can put this solution on YOUR website!
.

For any quadratic function

    f(x) = ax^2 + bx + c

with the negative leading coefficient "a", it gets the maximum at  x = .



In your case, the quadratic function is  h(t) = -4.9*t^2 + 18t + 8,

so the coefficients are  a = -4.9  and  b = 18.



Thus it gets the maximum at  t =  = 1.837 seconds.



ANSWER.  It will take 1.837 seconds to get the maximum height.

Solved.

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For related issues and problems, see the lessons
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
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    - Briefly on finding the vertex of a parabola

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in this site.


Answer by Edwin McCravy(20065)   (Show Source): You can put this solution on YOUR website!
If we plot the graph, we get



We use the vertex formula to find the value of t at the maximum height,
which is reached at the vertex.



Round to 1.837 seconds to get to the maximum height.

Edwin
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
we have

where
is the in meters above the ground
is the in seconds
This is a open , so the is a .
The number of seconds it takes for the ball to reach the maximum height is equal to the -coordinate of the vertex.
Convert the given function to vertex form:

......factor
.......complete the squares
......, =>=>=>=>

------

...........



=>the vertex is the point
(,)=(, )-> is coordinate
The number of seconds it takes for the ball to reach the maximum height is .

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