SOLUTION: A ball is thrown vertically upward from the ground with an initial velocity of 134 ft/sec. Use the quadratic function h(t) = −16t2 + 134t + 0 to find how long it will take fo

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Question 1157715: A ball is thrown vertically upward from the ground with an initial velocity of 134 ft/sec. Use the quadratic function
h(t) = −16t2 + 134t + 0
to find how long it will take for the ball to reach its maximum height (in seconds), and then find the maximum height (in feet)
Found 2 solutions by Boreal, josmiceli:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The maximum height of a quadratic occurs when t=-b/2a (vertex) where here b=134 and a=-16
so at -134/-32 or 4.1875 seconds
h(4.1875)=-280.5625+561.125
=280.5625 or 281 feet

graph%28300%2C300%2C-5%2C10%2C-50%2C300%2C-16x%5E2%2B134x%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h%28t%29+=+-16t%5E2+%2B+134t+
The vertex ( maximum ) is located midway between
the roots where +h%28t%29+=+0+
+h%28t%29+=+t%2A%28+-16t+%2B+134+%29+
+0+=+t%28+-16t+%2B+134+%29+
the roots are:
+t+=+0+
and
+-16t+%2B+134+=+0+
+16t+=+134+
+t+=+8.375+ sec
-------------------------
+%28+8.375+%2B+0++%29+%2F+2+=+4.1875+
+t%5Bmax%5D+=+4.1875+ ( time to reach maximum height )
Plug this back into equation
+h%28t%29+=+t%2A%28+-16t+%2B+134+%29+
+h%5Bmax%5D+=+4.1875%2A%28+-16%2A4.1875+%2B+134+%29+
+h%5Bmax%5D+=+4.1875%2A%28+-67+%2B+134+%29+
+h%5Bmax%5D+=+280.56+ ft ( maximum height )
check:
Here's the plot:
+graph%28+400%2C+400%2C+-2%2C+10%2C+-30%2C+320%2C++-16x%5E2+%2B+134x+%29+
Looks OK