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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. The maximum value achieved by the function is represented by the vertex. Use factoring to answer the following:

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?

Hint: because parabolas are symmetric, the vertex of a parabola is halfway between the zeroes of the quadratic.

 Jan 15, 2019
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When h= 0   the ball has not been yet thrown AND it is when the ball has returned and landed (the two zeroes)

 

h = 0 :

       0 = -8t^2 + 40t   factoring yields

           0= -8t (t - 5)      so t = 0 or 5     are the zeroes of the equation

 

Midpoint between the zeroes is    t = 2.5 sec   for the highest point

First of the ordered pair is 2.5    sub in 2.5 to find the highest the ball reaches

          h = -8(2.5)^2 + 40(2.5) = 50    feet          oredered pair is   (2.5 sec , 50 ft)

 Jan 15, 2019

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