SOLUTION: Tom throws a ball into the air. The ball travels on a parabolic path represented by the equation h = -8t^2 + 40t, where h represents the height of the ball above the ground and t r

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Tom throws a ball into the air. The ball travels on a parabolic path represented by the equation h = -8t^2 + 40t, where h represents the height of the ball above the ground and t r      Log On


   

Question 1025172: Tom throws a ball into the air. The ball travels on a parabolic path represented by the equation h = -8t^2 + 40t, where h represents the height of the ball above the ground and t represents the time in seconds.
How many seconds does it take the ball to reach its highest point?
What ordered pair represents the highest point that the ball reaches as it travels through the air?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+h+=+-8t%5E2+%2B+40t+
The x-value of the vertex is at:
+t%5Bv%5D+=+-b%2F%282a%29+ where
+a+=+-8+
+b+=+40+
+t%5Bv%5D+=+-40+%2F+%28+2%2A%28-8%29+%29+
+t%5Bv%5D+=+40%2F16+
+t%5Bv%5D+=+5%2F2+
Plug this valuie back into the equation
to get +h%5Bv%5D+
+h%5Bv%5D+=+-8t%5E2+%2B+40t+
+h%5Bv%5D+=+-8%2A%285%2F2%29%5E2+%2B+40%2A%285%2F2%29+
+h%5Bv%5D+=+-8%2A%2825%2F4%29+%2B+200%2F2+
+h%5Bv%5D+=+-50+%2B+100+
+h%5Bv%5D+=+50+
-------------------
It takes 2.5 sec for the ball to reach the highest point
The ordered pair of the vertex point is:
( 2.5, 50 )
-------------
Here's the plot:
+graph%28+400%2C+400%2C+-1%2C+6%2C+-5%2C+55%2C+-8x%5E2+%2B+40x+%29+