A ball is thrown into the air with an upward velocity of 40 ft/s. Its height h in feet after t seconds is given by the function h = - 16t2 + 40t + 10. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball's maximum height?

Question

Mathematics

Patience

23 January, 05:17

A ball is thrown into the air with an upward velocity of 40 ft/s. Its height h in feet after t seconds is given by the function h = - 16t2 + 40t + 10. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball's maximum height?

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Answers (1)

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Tristan Ramos · Answer 1

The maximum (or minimum) of a parabolic function would be it's vertex.

To find the vertex use the formula x = - b / (2a), after finding x, plug x back into the function to find y.

The function needs to be in standard form ax^2 + bx + c, so

a = - 16, b = 40

x = - 40 / (2*-16) = 1.25

y = - 16 (1.25) ^2 + 40 (1.25) + 10

y = - 25 + 50 + 10

y = 35

The maximum height is the y value of the vertex. 35 feet is the answer.