Question

example 3

1. 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.

Explanation:

Step1: Find x - intercepts

The x - intercepts are the points where the graph crosses the x - axis (y = 0). By looking at the graph, the x - intercepts are approximately x = 0 and x = 5.5. In the context of the football, x = 0 is when the football is first kicked, and x = 5.5 is when the football hits the ground.

Step2: Find y - intercept

The y - intercept is the point where the graph crosses the y - axis (x = 0). From the graph, the y - intercept is approximately y = 6. This means the initial height of the football when it is kicked is 6 meters.

Step3: Determine where the function is positive and negative

The function is positive when y>0. From the graph, the function is positive for 0 < x < 5.5. This means the football is above the ground during this time interval. The function is never negative in this context since the height of the football (y - value) cannot be negative in terms of real - world height above the ground.

Answer:

x - intercepts: approximately x = 0 and x = 5.5; y - intercept: approximately y = 6; The function is positive for 0 < x < 5.5 and never negative. The x = 0 x - intercept is when the football is kicked, x = 5.5 is when it hits the ground, and y = 6 is the initial height of the football.