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A basketball is thrown upwards. The height f(t), in feet, of the basketball at time t, in seconds, is given by the following function:


f(t) = −16t2 + 16t + 32


Which of the following is a reasonable domain of the graph of the function when the basketball falls from its maximum height to the ground?

0.5 < t < 1

0.5 < t < 2

1 < t < 2

1 < t < 1.5

Respuesta :

sqdancefan

Answer:

  0.5 < t < 2

Step-by-step explanation:

The function reaches its maximum height at ...

  t = -b/(2a) = -16/(2(-16)) = 1/2 . . . . . . where a=-16, b=16, c=32 are the coefficients of f(t)

The function can be factored to find the zeros.

  f(t) = -16(t^2 -1 -2) = -16(t -2)(t +1)

The factors are zero for ...

  x = -1 and x = +2

The ball is falling from its maximum height during the period (0.5, 2), so that is a reasonable domain if you're only interested in the period when the ball is falling.

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