Question

football the graph shows the height of a football after being kicked. 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. the x - intercept is select choice. this means that the football will hit the ground after select choice seconds. the y - intercept is select choice. this means that at time select choice the football was at a height of select choice meters. the graph shows that the function is select choice which means that that the football is in the air for select choice seconds.

Explanation:

Step1: Identify x - intercept

The x - intercept is the value of x when y = 0. Looking at the graph of the height of the football over time, the x - intercepts are the times when the height of the football is 0 (it hits the ground). By observing the graph, the x - intercepts are approximately x = 0 and x = 9 seconds. The relevant x - intercept for when the football hits the ground after being kicked is x = 9 seconds.

Step2: Identify y - intercept

The y - intercept is the value of y when x = 0. When x = 0 (at the moment of kicking), from the graph, the y - intercept is approximately y = 0.5 meters. This means the football was at a height of 0.5 meters when it was kicked.

Step3: Determine the nature of the function

The function is positive when the graph is above the x - axis (height > 0) and negative when below the x - axis (not applicable in this real - world context as height can't be negative in this situation). The function is positive for 0 < x < 9, which means the football is in the air for 9 seconds.

Answer:

The x - intercept is 9 seconds. This means that the football will hit the ground after 9 seconds.
The y - intercept is 0.5 meters. This means that at time 0 (when kicked), the football was at a height of 0.5 meters.
The function is positive for 9 seconds. This means that the football is in the air for 9 seconds.