Water coming out from a fountain is modeled by the function f(x) = −x2 + 5x + 4 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 = 3 to x = 5 represent?

f(5) = -x^2 +5x +4

f(5) = -5^2 +5*5 +4

f(5) = -25+25 +4

f(5) = 4

f(3) = -x^2 +5x +4

f(3) = -3^2 +5*3+4

f(3) = -9+15+4

f(3) = 6+4

f(3) = 10

{ f(3) - f(5) } ÷ 2

{ 10-4 } ÷ 2

6 ÷ 2

3

The water falls down with an average speed of 3 feet per second from 3 seconds to 5 seconds.

I got this option when I took the test and I got it right.

The water falls down with an average speed of 3 feet per second from 3 seconds to 5 seconds would be the answer you're looking for, I wont prove the answer because the other guy has shown all work and it is correct!