Question

A model for the height of an arrow shot into the air is $h(t)=-16 t^{2}+72 t+5$ where $t$ is time and $h$ is height. Without graphing, consider the function's graph. a. What can you learn by finding the graph's intercept with the $h$ -axis? b. What can you learn by finding the graph's intercept(s) with the $t$ -axis?

Name: Problem 43, Chapter 5: Algebra 2
Uploaded: 2023-11-11T16:44:59-08:00
Channel: Stephanie Hirsch
Description: A model for the height of an arrow shot into the air is h(t)=-16 t^2+72 t+5 where t is time and h is height. Without graphing, consider the function's graph. a. What can you learn by finding the graph's intercept with the h -axis? b. What can you learn by finding the graph's intercept(s) with the t -axis?

   A model for the height of an arrow shot into the air is $h(t)=-16 t^{2}+72 t+5$ where $t$ is time and $h$ is height. Without graphing, consider the function's graph.
a. What can you learn by finding the graph's intercept with the $h$ -axis?
b. What can you learn by finding the graph's intercept(s) with the $t$ -axis?

Algebra 2

Prentice Hall, Basia… 1st Edition

Chapter 5, Problem 43

Instant Answer

Solved by Expert Stephanie Hirsch

11/11/2023

Step 1

This gives us $h(0)=-16(0)^2+72(0)+5=5$. This means that the arrow was shot initially from a height of 5 units. Show more…

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A model for the height of an arrow shot into the air is $h(t)=-16 t^{2}+72 t+5$ where $t$ is time and $h$ is height. Without graphing, consider the function's graph. a. What can you learn by finding the graph's intercept with the $h$ -axis? b. What can you learn by finding the graph's intercept(s) with the $t$ -axis?

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Key Concepts

Quadratic Function Graph Analysis

A quadratic function produces a parabolic graph, and understanding its general features—such as its vertex, axis of symmetry, and intercepts—is crucial for interpreting its behavior. This analysis helps in predicting the maximum or minimum values and the overall dynamics of the system being modeled.

X-Intercepts

The x-intercepts are the points where the graph crosses the horizontal axis, which are the solutions where the function equals zero. In physical contexts, these intercepts can represent significant events, such as the time at which an object reaches ground level or a process comes to an end.

Y-Intercept

The y-intercept is the point where the graph crosses the vertical axis, which represents the value of the function when the independent variable is zero. In many applications, such as projectile motion, the y-intercept provides the initial condition of the system, showing where the process started.

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