SOLUTION: A ball is thrown upward into the air with an initial velocity of 64 ft/s. If h gives the height of the ball at the time t, then the equation relating h and t is h=-16t^2+64t Fi

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A ball is thrown upward into the air with an initial velocity of 64 ft/s. If h gives the height of the ball at the time t, then the equation relating h and t is h=-16t^2+64t Fi      Log On


   

Question 1110482: A ball is thrown upward into the air with an initial velocity of 64 ft/s. If h gives the height of the ball at the time t, then the equation relating h and t is
h=-16t^2+64t
Find the maximum height the ball will attain.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When the equation has the form +y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
then the x-value of the vertex ( either max or min ) is
located at +x%5Bv%5D+=+-b%2F%282a%29+
-----------------------------------
You are given:
+h+=+-16t%5E2+%2B+64t+
+t%5Bmax%5D+=+-64%2F%282%2A%28-16%29%29+
+t%5Bmax%5D+=+64%2F32+
+t%5Bmax%5D+=+2+ sec
------------------------------
Plug this back into equation to get +h%5Bmax%5D+
+h%5Bmax%5D+=+-16%2A2%5E2+%2B+64%2A2+
+h%5Bmax%5D+=+-64+%2B+64%2A2+
+h%5Bmax%5D+=+64+
The maximum height is 64 ft
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check:
plot the equation:
+graph%28+400%2C400%2C-1%2C5%2C+-10%2C+80%2C+-16x%5E2+%2B+64x+%29+
looks right