7.14.5 Identifying Key Features of Graphed Functions

Algebra 17.14.5 Identifying Key Features of Graphed Functions

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

Since the equation is in factored form, we can tell that the graph intersects the horizontal axis at two points. Use this information to find the zeros of the function. Explain or show your reasoning.

Find one of the zeros of the functions using $(- 16 t - 2)$ .

-0.125 or $- \frac{1}{8}$ . From the factored form, we can tell that the graph intersects the horizontal axis at $t = - 0.125$ or $- \frac{1}{8}$ . The zero of the function is the same value.

Find one of the zeros of the functions using $(t - 1)$ .

1. From the factored form, we can tell that the graph intersects the horizontal axis at t=1. The zero of the function is the same value.

What do the zeros tell us in this situation?

Compare your answer:

The zeros mean the time in seconds when the ball is on the ground.

Are both zeros meaningful?

No. Only one of them is meaningful. The negative zero doesn't mean anything here.

From what height, in feet, is the beach ball thrown? Explain or show your reasoning.

Compare your answer:

2. The height when $t = 0$ is $(- 16 (0) - 2) (0 - 1) = (- 2) (- 1) = 2$ . If you graph the function, the graph shows a $y$ -intercepts of $(0, 2)$ .

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- Publication date: Jun 4, 2025
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