SOLUTION: The height of a ball that is thrown upward is given by h(t) = {{{ 16t^2 + 68t }}} where t is in seconds and height is in feet. The maximum height the ball reaches is ____ f

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Question 906158: The height of a ball that is thrown upward is given by
h(t) = +16t%5E2+%2B+68t+
where t is in seconds and height is in feet. The maximum height the ball reaches is ____ feet, when t = ____ seconds.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The equation should be:
+h%28t%29+=+-16t%5E2+%2B+68t+
The minus sign is for the
downward pull of gravity
-----------------------
The formula for +t%5Bmax%5D+
is:
+t%5Bmax%5D+=+-b%2F%282a%29+
where:
+a+=+-16+
+b+=+68+
+t%5Bmax%5D+=+-68%2F%282%2A%28-16%29%29+
+t%5Bmax%5D+=+2.125+
Now find +h%5Bmax%5D+
---------------------
+h%5Bmax%5D+=+-16%2A2.125%5E2+%2B+68%2A2.125+
+h%5Bmax%5D+=+-72.25+%2B+144.5+
+h%5Bmax%5D+=++72.25+
--------------------
The max height is 72.25 ft
when the time is 2.125 sec
-------------------------
Here's the plot:
+graph%28+400%2C+400%2C+-1%2C+7%2C+-10%2C+100%2C+-16x%5E2+%2B+68x+%29+