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A ball is projected upward from the top of a 90 foot building at a velocity of 64 feet per second. The ball's height above the ground below the building is described by the function h(t)=-16t^2 + 64t + 90 , with t being the time in seconds after the ball is projected upward. a.) Determine the amount of the vertical intercept, and interpret what this means in the context of the problem (in terms of seconds and feet above the ground). b.) Determine the amount of all horizontal intercepts (if any) , and interpret what they mean in teh context of the problem (in terms of seconds and feet above the ground). c. Write the coordinates of the vertex. Interpret what these numbers mean in the context of the problem. d. If nothing stops the ball before, then how much time elapses until the ball hits the ground below the building?

Answer 1

to find the vertical intercept take t=0

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90 feet indicates the initial height of the ball (that is building's height)

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to find horizontal intercepts take h=0

...................horizontal intercept

take an only positive value

which means after seconds ball hits the ground

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compare with vertex form of the parabola

so here vertex is  

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which means at second ball achieves a maximum height of feet

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here one horizontal intercept is

which means after seconds ball hits the ground