Water coming out from a fountain is modeled by the function f(x) = -x2 + 6x + 6 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.
what does the average rate of change of f(x) from x = 2 to x = 5 represent?
the water travels an average distance of 4 feet from 2 seconds to 5 seconds.
the water travels an average distance of 1 foot from 2 seconds to 5 seconds.
the water falls down with an average speed of 2 feet per second from 2 seconds to 5 seconds.
the water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

answer: y = -12x + 108

step-by-step explanation: do (y = m x+b) formula.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."