Question

Can someone help me out!! (:

Water coming out from a fountain is modeled by the function f(x) = -x2 + 7x + 5 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 = 4 to x = 6 represent?

Answer 1

The water travels an average distance of 3 feet from 4 seconds to 6 seconds.
The water falls down with an average speed of 3 feet per second from 4 seconds to 6 seconds.
The water travels an average distance of 5 feet from 4 seconds to 6 seconds.
The water falls down with an average speed of 5 feet per second from 4 seconds to 6 seconds.

Answer 2

@Jadeishere

Answer 3

First, calculate the value of f(x) at x = 4 and x = 6.

Answer 4

Make sure you use this equation, though:
\[-(x)^2 + 7x + 5\]
The minus sign stays in front of the first term.

Answer 5

would it be 64+72+5? im not sure..?? @LukeBlueFive

Answer 6

Just plug in x = 4 into:
\[-(x)^2 + 7x + 5\]
To get:
\[-(4)^2 + 7*4 + 5\]
Now square the four:
\[-16 + 7*4 + 5\]
Think you can take it from here? Let me know if you need some more help.

Answer 7

alright so i just solve -16+7*4+5=17?? is that right?? im no good at math.. ): @LukeBlueFive

Answer 8

That's right, you're doing great. The height of the water from the fountain after 4 seconds (x = 4) is 17 feet. Now, plug in x = 6 into the same equation and solve it again.

Answer 9

That will give you the height of the fountain after 6 seconds.

Use x = 6 in the following equation:
\[-(x)^2 +7x + 5\]

Answer 10

so -16+7*6+5=42? is that right?

Answer 11

36+7x+5=48x???? @LukeBlueFive

Answer 12

Oh, very close. You forgot the minus sign in front of the 36, and you had the rest of it correct (7*6 + 5).

Answer 13

ohh alright so the answer would be D? @LukeBlueFive

Answer 14

No, how did you get that answer?

When x = 6, f(x) = -36 + 7*6 + 5.

Answer 15

Once we have that value, we can find out if the fountain was increasing or decreasing in height, and how quickly. Then we can find the answer.

Answer 16

i give up i still have alot more problems to go thanks though.. ): @LukeBlueFive

Answer 17

Sorry I wasn't more of a help.

Answer 18

would you mind giving me a hint...i dont want to get any wrong... @LukeBlueFive

Answer 19

Sure, after four seconds the height of the fountain is 17 feet. After six seconds, the height of the fountain is 11 feet. During these two seconds, how much did the fountain drop by?

Answer 20

dropped by 6 @LukeBlueFive

Answer 21

Correct, so it dropped 6 feet over two seconds. How many feet did it drop per second?

Answer 22

3 feet dropped @LukeBlueFive

Answer 23

so b?

Answer 24

Congrats, you got it!