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The equation y = (-16t -2)(t-1) represents the height in feet of a beach ball thrown by a child as a function of time, t, in seconds.

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Anonymous
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1) Find the zeros of the function. Explain or show your reasoning.

2) What do the zeros tell us in this situation? Are both zeros meaningful?

3) From what height is the beach ball thrown? Explain or show your reasoning.

Sangeetha Pulapaka
0

1) The zeros of the function y = (-16 t - 2)(t-1) can be found by plugging in y = 0, to get (-16 t - 2)(t -1) = 0

\Rightarrow -16 t - 2 = 0 and t - 1 = 0

\Rightarrow t = \frac{-2}{16} = \frac{-1}{8} and t = 1.


So 1, -1/8 are the zeros of the function.


2) It is given that the height of the ball, in feet, is a function of time, t, in seconds. So time lies on the x-axis and the height lies on the y-axis (1,0) says that when the time is 1 second the height of the beachball is 0. Negative value of zero is not realistic in this situation because time in seconds cannot be a negative value. So t = 1 is the only meaningful zero.


3) This can be found by finding the y-intercept of the given function. We plug in t = 0 in the given equation to find the height at which the beach ball is thrown.

Given

y = (-16 t -2)(t-1)  

Plugging in t = 0,

y = (-2)(-1) = 2

So when the time is zero, the height of the beachball is 2 feet. The ball was thrown from a height of 2 feet.