Question

Quadratic equation help :)

Answer 1

Using complete sentences, explain how to find the average rate of change for f(x) from x = 4 to x = 7.

The equation is y = 3(7-2)^2 + 98. I know that you start with f(4) = 3(4 - 2)^2 + 98 and f(7) = 3(7 - 2)^2 + 98, I'm just not sure where to go from here.

Answer 2

what is the function??

Answer 3

f(x) = 3(7-2)^2 + 98

Answer 4

that is not a function, that is just a number
is there an \(x\) in it somewheres?

Answer 5

Sorry, I meant f(x) = 3(x-2)^2 + 98

Answer 6

ok what is \(f(7)\) ?

Answer 7

I'm not totally sure lol. Can we just start from scratch with f(x) = 3(x-2)^2 + 98?

Answer 8

sure

Answer 9

\[f(x)=3(x-2)^2+98\] and so
\[f(7)=3(7-2)^2+98=3\times 5^2+98=3\times 25+98=75+98=176\]

Answer 10

in brief, \(f(7)=176\)

Answer 11

now you need \(f(4)\)

Answer 12

Okay, I'm still trying to figure out what you just did haha

Answer 13

where i saw an \(x\) i replaced it by a \(7\) and then computed the resulting number

Answer 14

I get replacing the x with 7, but I don't get = 3 × 52 + 98 = 3 × 25 + 98 = 75 + 98 = 176

Answer 15

should be \(3\times 5^2\) not \(3\times 52\)

Answer 16

\[3(7-2)^2+98\]What he did first was evaluate 7 - 2 = 5.\[3(5)^2+98\]Then he did 5^2=25.\[3(25)+98\]Then he did 3 * 25 = 75.\[75+98\]Which is 176.

Answer 17

what @bagajr said

Answer 18

Okay, I that makes sense. Only thing I don't get from that is the 5 (from 7 - 2 = 5)

Answer 19

what else could five minus two be?

Answer 20

I don't understand. Are you saying you don't understand why 7 minus 2 gives 5?

Answer 21

Wow I feel really stupid right now lol. I'm sorry, I wasn't paying attention at all. Never mind haha

Answer 22

That's alright, you must have just been overthinking things, lol

Answer 23

Yeah, we can go with that haha. Okay, so I understand all of that, so I'll try f(4) really quick.

Answer 24

\[4 - 2 = 2\]
\[3(2)^2 + 98\]
\[2^2 = 4\]
\[3(4) + 98\]
\[3 * 4 = 12\]
\[12 + 98 = 110\]
f(4) = 110?
Is that right?

Answer 25

Yes

Answer 26

Alright cool! There's one more if you wouldn't mind :)

Answer 27

To find the rate of change between two points (in this case, x=4 and x=7), find the slope between them. Do you know how to do that?

Answer 28

*average rate of change

Answer 29

Oh yeah, forgot about that part lol. I think so, one sec.

Answer 30

I think it's 22?

Answer 31

Correct

Answer 32

Alright, thanks a lot! I might need help with the other, if I do, would you mind? :)

Answer 33

Okay, are you going to post it right here?

Answer 34

No, I'll ask another question then mention you, that way I can give you another medal lol