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

Algebra ->  Inverses -> 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      Log On


   

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(52817) About Me  (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 = -b%2F%282a%29.



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 = -18%2F%282%2A%28-4.9%29%29 = 1.837 seconds.



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

Solved.

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Answer by Edwin McCravy(20060) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
we have
h%28t%29+=+-4.9t%5E2+%2B+18t+%2B+8
where
h%28t%29+is the height in meters above the ground
t is the time in seconds
This is a vertical+parabola open downward, so the vertex is a maximum.
The number of seconds it takes for the ball to reach the maximum height is equal to the x-coordinate of the vertex.
Convert the given function to vertex form:
h%28t%29+=+-4.9t%5E2+%2B+18t+%2B+8
h%28t%29+=+%28-4.9t%5E2+-+18t+%29%2B+8......factor -4.9
h%28t%29+=+-4.9%28t%5E2+-+%2818%2F4.9%29t+%29%2B+8.......complete the squares
h%28t%29+=+-4.9%28t%5E2+-+%2818%2F4.9%29t%2Bb%5E2+%29-%28-4.9%29b%5E2%2B+8......a=1, 2ab=+%2818%2F4.9%29=>2b=+%2818%2F4.9%29=>b=+%2818%2F4.9%29%2F2=>b=+%2818%2F9.8%29=>b=180%2F98=90%2F49

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4.9%2890%2F49%29%5E2=810%2F49+=+16.531
h%28t%29+=+-4.9%28t+-+90%2F49%29%5E2+%2B16.531%2B+8...........90%2F49=1837
h%28t%29+=+-4.9%28t+-+1.837%29%5E2+%2B24.531


=>the vertex is the point
(h,k)=(1.8, 24.531)-> h is x coordinate
The number of seconds it takes for the ball to reach the maximum height is 1.837.