Question

example 3

1. football the graph shows the height of a football after being thrown. use the graph to estimate the x - and y - intercepts of the function, where the function is positive and negative, and interpret the meanings in the context of the situation.
2. earnings the graph shows the amount of money ryan earns. use the graph to estimate the x - and y - intercepts of the function, where the function is positive and negative, and interpret the meanings in the context of the situation.

Explanation:

10. Football

Step1: Find x - intercept

The x - intercept is the time when the height of the football is 0. Looking at the graph, it seems the x - intercept is around 9 seconds. This means the football hits the ground after approximately 9 seconds.

Step2: Find y - intercept

The y - intercept is the height of the football at time t = 0. From the graph, the y - intercept is around 0 feet. This implies the football starts at ground level.

Step3: Determine positive and negative parts

The function is positive when the height of the football is above the ground (y>0), which is from t = 0 to t≈9 seconds. It is negative nowhere in this real - world context as height cannot be negative in terms of the physical situation.

Step1: Find x - intercept

The x - intercept is the time when Ryan's earnings are 0. From the graph, it appears to be at around 10 hours. This could mean that after 10 hours of some activity related to earning, the total earnings return to 0 (perhaps some kind of investment or cost - recovery situation).

Step2: Find y - intercept

The y - intercept is the amount of money Ryan has at time t = 0. From the graph, the y - intercept is around 200 dollars. This might represent an initial amount of money Ryan has before starting the activity related to the earnings.

Step3: Determine positive and negative parts

The function is positive when Ryan has positive earnings (y>0), which is from t = 0 to t = 10 hours. It is negative nowhere in this context as earnings are represented as non - negative values in this graph.

Answer:

x - intercept: approximately 9 seconds (football hits the ground); y - intercept: approximately 0 feet (football starts at ground level); positive from t = 0 to t≈9 seconds, negative: none.

11. Earnings