Question

Help please
water is coming out of a fountain is modeled by the function f(x)=-x^2+8x+2 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=1 to x=4 represent

Answer 1

Answer choices:


The water travels an average distance of 3 feet from 1 second to 4 seconds.

The water travels an average distance of 2 feet from 1 second to 4 seconds.

The water rises up with an average speed of 3 feet per second from 1 second to 4 seconds.

The water rises up with an average speed of 2 feet per second from 1 second to 4 seconds.

Answer 2

It either one of the last two answer choices. But what do you think @Glorenda49

Answer 3

\[f(b)-f(a)\div b-a\] that's all i know is the average rate of change formula @SCARLET_SPIDER

Answer 4

I don't understand how to get to that point

Answer 5

Than I' am guessing the answer is the last choice @Glorenda49

Answer 6

@campbell_st can you please help me?

Answer 7

the average rate of change

you need to 1st find f(1) and then f(4)

is that ok...?

Answer 8

yeah i will also go for the last one as the answer

Answer 9

f(1) just means substitute x = 1 into the equation and get a value

f(4) just substitute x = 4 and get a value

Answer 10

Yeah so I was correct taking an educated guess

Answer 11

Glorenda have you found the values yet?

Answer 12

f(x) at x=1 and at x=4

Answer 13

but note that f(x) represents height in feet, and x represents time in seconds

Answer 14

also note that speed is worked out to be distace/time

Answer 15

in other words heigth/time
so,
workout speed at x=1 and x=4
and get the difference

Answer 16

if you are having trouble, this is what it looks like

\[f(1) = -(1)^2 + 8(1) + 2\]

and

\[f(4) = -(4)^2 + 8(4) + 2\]

a diagram looks like