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. 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?

The zeros of a function f(x) are the values of x such that f(x) = 0.

The solutions are:

a) The zeros are t = 1 and t = -1/8

b) these represent the times at which the height of the ball is zero.

Here we have:

y = (-16*t - 2)*(t - 1)

a) Finding the zeros is trivial, we will have two zeros, one for each of the values of t that make the parentheses equal to zero.

One zero is when:

-16*t - 2 = 0

-16*t = 2

t = 2/-16 = -1/8

The other zero is when:

t - 1 = 0

t = 1

Then the two zeros are t = -1/8 and t = 1.

b) What do the zeros tell us in this situation?

Well, the equation represents the height of an object, thus the zeros are the values at which the object is on the ground (at a height of zero).

But not the two zeros are meaningful, as one is a negative time, so it can be discarded.

If you want to learn more, you can read:

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y = (-16t-2)(t-1)

To find the zeros, let's set y = 0 and separate these two expressions in parenthesis with the zero product property.

0 = -16t-2

0 = t-1

Now let's solve for t and get two zeros.

0 = -16t-2

2 = -16t

t = -1/8

0 = t-1

t = 1

1. Our two zeros are t = -1/8 and t = 1.

2. The two zeros are not both meaningful! Remember that this is modeling time, and we don't really care about -1/8 seconds. We don't need that negative time measurement, so we just want to know what's happening at 1 second. And at one second, the ball is on the ground. Great, so we know that height of ball = 0 after 1 second.

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