SOLUTION: A fountain shoots water from a nozzle at its base. The height h, in feet, of the water above the ground t seconds after it leaves the nozzle is given by the function h(t) = –16t^2

Algebra ->  Equations -> SOLUTION: A fountain shoots water from a nozzle at its base. The height h, in feet, of the water above the ground t seconds after it leaves the nozzle is given by the function h(t) = –16t^2       Log On


   



Question 1058957: A fountain shoots water from a nozzle at its base. The height h, in feet, of the water above the ground t seconds after it leaves the nozzle is given by the function h(t) = –16t^2 + 15t + 6. What is the maximum height of the water? Round to the nearest tenth.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use the formula for the vertex
which is:
+t%5B+max+%5D+=+-b%2F%282a%29+
+a+=+-16+
+b+=+15+
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+t%5Bmax%5D+=+-15%2F%282%2A%28-16%29%29+
+t%5Bmax%5D+=+15%2F32+
Plug this value back into equation
to find +h%5Bmax%5D+
---------------------------------
+h%5Bmax%5D+=+-16%2A%2815%2F32%29%5E2+%2B+15%2A%2815%2F32%29+%2B+6+
+h%5Bmax%5D+=+-3.515625+%2B+7.03125+%2B+6+
+h%5Bmax%5D+=+9.515+
The maximum height of the water is 9.5 ft
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here's the plot:
+graph%28+400%2C+400%2C+-1%2C+3%2C+-2%2C+12%2C+-16x%5E2+%2B+15x+%2B+6+%29+