Question

Water coming out of a fountain is modeled by the function F(X) = -X to the power of 2+ 8X plus to wear f(X)represents the height and feet of the water from the fountain at different times X and seconds what does the average rate of change F(X) from X equals one to ask equals four represent

Answer 1

geez - ever think of using actual algebra? Either your typing or your dictation is really bad.
f(x) = -x^2 + 8x + "to wear"
you want the average rate of change of f(x) for 1 ≤ x ≤ 4
As usual, that is
(f(4)-f(1)) / (4-1)
so plug in your numbers.

Answer 2

Having been exposed to many students of this era that can no longer speak or spell properly, let me guess that by

"F(X) = -X to the power of 2+ 8X plus to wear f(X)represents the height and feet of the water"

Parker means:
F(x) = -x^2 + 8x + 2, where f(x)represents the height of the water"

Still have no idea what the "feet of the water" have to do with it.