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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.

Respuesta :

Answer:

Time to highest point: 5/2, or 2.5 seconds

Ordered pair: (5/2, 50)

Step-by-step explanation:

Find the vertex of h(t). This will be the highest point of the ball

Find the x coordinate of the vertex with the formula: x = -b/(2a)

x = -40/[2(-8)] = -40/-16 = 5/2

to find the y value, plug 5/2 into the equation and solve

h(5/2) = -8(5/2)² + 40(5/2)

   h(5/2) = -8(25/4) + 200/2

          h(5/2) = -200/4 + 100

             h(5/2) = 50

So the ball reached a maximum height of 50 feet

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