Answer:
1) Zero based on (-16·t - 2) is t = -1/8 second
2) Zero based on (t - 1) is t = 1 second
Explanation:
The given functions representing the height of the beach ball the child throws as a function of time are;
y = (-16·t - 2)·(t - 1) and y = -16·t² + 14·t + 2
We note that (-16·t - 2)·(t - 1) = -16·t² + 14·t + 2
Therefore, the function representing the height of the beachball, 'y', is y = (-16·t - 2)·(t - 1) = -16·t² + 14·t + 2
The zeros of a function are the values of the variables, 'x', of the function that makes the value of the function, f(x), equal to zero
In the function of the question, we have;
y = (-16·t - 2)·(t - 1) = -16·t² + 14·t + 2
The above equation can be written as follows;
y = (-16·t - 2) × (t - 1)
Therefore, 'y' equals zero when either (-16·t - 2) = 0 or (t - 1) = 0
1) The zero based on (-16·t - 2) = 0, is given as follows;
(-16·t - 2) = 0
∴ t = 2/(-16) = -1/8
t = -1/8 second
The zero based on (-16·t - 2) is t = -1/8 second
2) The zero based on (t - 1) = 0, is given as follows;
(t - 1) = 0
∴ t = 1 second
The zero based on (t - 1) is t = 1 second