Question

The graph of a function 'f' is shown below.

Use the graph of the function to find its average rate of change from x=-2 to x=4.

Simplify your answer as much as possible.

http://i65.tinypic.com/8zg2l3.jpg

Please help I'm super confused.

Answer 1

@ganeshie8 @pooja195

Answer 2

please help

Answer 3

I can help you :D

Answer 4

@kgrendel0324 omg thank you

Answer 5

Tell me both y values for both x values

Answer 6

Are there any answer choices?

Answer 7

x values= -2,1,-5,4,-8
y values= 3,0,0,-9,-9
I think this is right im not sure

Answer 8

and no its fill in the blank

Answer 9

it wold have made it easier

Answer 10

@kgrendel0324

Answer 11

ok you need to plug this in

Answer 12

into what?

Answer 13

wait not can you find the equation for the function

Answer 14

ok dont u have to find the function first before you find the average rate of change?

Answer 15

yes thats what you need to do

Answer 16

ok that where im stuck. Finding the function.

Answer 17

I'm so sorry. I have to go. :( good luck

Answer 18

Rate of change = y2-y1/x2-x1
Understand?

Answer 19

no yeah i understand how to do rate of change

Answer 20

Just not finding the function

Answer 21

From what i remember its a parabola that opens downward

Answer 22

it is

Answer 23

I have all the points already
im just stuck on the function

Answer 24

So the normal equation for a parabola is x^2, and when it opens downward, it's -x^2

Answer 25

But I don't know where it starts, ill try and load the picture again

Answer 26

it starts a (-2,3)

Answer 27

thats the vertex i think

Answer 28

im SO BAD AT MATH IM SORRY

Answer 29

It's okay! You're doing alright. I don't really use the vocab words for it, I just plpay it as is

Answer 30

OK thanx so much for ur help

Answer 31

No problem

Answer 32

alright, so its 2 units to the left and 3 units upward

Answer 33

yes exactly

Answer 34

You are correct, the vertex is (-2, 3)

Answer 35

at least im on the right track

Answer 36

So when you shift vertically, moving left or right on the x-axis, if it moves to the right the number is negative

Answer 37

Kinda the opposite of what is expected

Answer 38

yeah i get it

Answer 39

why is that though?

Answer 40

*sorry i meant horizontal shift before

Answer 41

yeah that makes more sense

Answer 42

And I'd guess because it flips it over the axis or something but im not actually sure why its the opposite sign

Answer 43

mmm ok so how would I find the function so I can find the rate of change

Answer 44

So when you have a horizontal and vertical shift, the vertical part goes within the parentheses with the x and the vertical shift goes outside the parentheses

Answer 45

so -(x + 2)^2 +3

Answer 46

Do i solve that?

Answer 47

Thats your function

Answer 48

but doesn't it need simplifying?

Answer 49

I simplified it to x^2-4x-1 but idk

Answer 50

Nah it doesnt need simplifying to my knowledge. I know how to get the function, but i can look up how to get rate of change if you want?

Answer 51

no ik how to do that!

Answer 52

the function does look like it need simplification though

Answer 53

I mean, you can
-(x + 2)^2 + 3
(x+2)(x+2)
-(x^2 + 4x + 4) + 3 and so on

Answer 54

was my simplification correct or...?

Answer 55

is the average rate of change -2? @imnotarobot5

Answer 56

-x^2-4x-4 + 3
-x^2 -4x -1

Answer 57

sorry I missed the response! @ isa1xoxo

Answer 58

ok thank you!

Answer 59

Figure this one out? :)

Answer 60

yes thank you thank you