Question

Given the function f(x) = 2(x − 1)2 + 1, indicate the shifts that will affect the location of the vertex and explain what effect they will have. Use complete sentences.

f(x+3)
f(x) + 3
f(3x)
3•f(x)

Answer 1

I'm very lost

Answer 2

your functions is
\[f(x)=2(x-1)^{2} +1\]

???

Answer 3

The function is f(x) = 2(x − 1)^2 + 1

Answer 4

yes

Answer 5

anyone good at math im in 8th anyone above

Answer 6

f(x+3) = 2((x+3) - 1)^2 + 1

Answer 7

I just want to understand what I'm even doing.

Answer 8

f(x+3) = 2(x+2)^2 +1

Answer 9

see i just put in the (x+3) for the x ?

Answer 10

yeah

Answer 11

In the form
f(x) = a*(x - b)^2 + c

the b term shifts the graph sideways
the c term shifts the graph up and down
the a term streatches the graph or compresses it

Answer 12

So what tells me how the vertex changes?

Answer 13

So if you put in f(x+3) = 2((x+3) - 1)^2 + 1 you get

f(x+3) = 2(x+2)^2 +1

Answer 14

In that case the b term is now -2 (x-(-2))

Answer 15

so you changed the b term by a +3

Answer 16

alright so what is the vertex in the equation or have we not even found it. I'm terrible at algebra.

Answer 17

it will move the vertex, the whole graph for that matter, sideways to the left by 3 units

Answer 18

Ohhh okay I get it now.

Answer 19

the standard "Vertex form is"

y = a(x-h)^2 +k

where (h,k) is the vertex point

Answer 20

so you get the first movement from the f(x+3) ?

Answer 21

so the question is I have to explain why it affects it and how it affects it.

Answer 22

you are putting in (x+3) into the equation wherever you see x

Answer 23

the standard form has (x - h) so if you add 3, it is the same as (x - (-3)) so that is moving the graph -3 in the x direction

Answer 24

(The vertex is the minimum or maximum in a quadratic eq) btw

Answer 25

Okay what tells us how much the vertex changes when we do this

Answer 26

how much the (h,k) changes in

y = a(x-h)^2 +k

Answer 27

okay so now what is the (h,k) in the new equation

Answer 28

We have

f(x) = 2(x − 1)2 + 1

f(x+3) = 2((x+3) - 1)^2 +1

Answer 29

so the h term changes from -1 to a +2, so the graph shifts to the LEFT by 3 units

Answer 30

(x - h) = (x -(-2)) = (x+2) the plus 2 means LEFT (x -(-2)) the h term is minus 2

Answer 31

so in summary, f(x+3) shifts the graph to the left 3 units

Answer 32

Thank you i get it now

Answer 33

the second is easier

Answer 34

f(x) + 3, you are going to add 3 to the k term in
y = a(x-h)^2 +k

Answer 35

Shift the graph up by 3 units

Answer 36

f(x) + 3 = 2(x-1)^2 +1 +3

f(x) + 3 = 2(x-1)^2 + 4

(h,k) is the vertex, and the k value increased by 3 units, (SHift UP 3 units)

Answer 37

for f(3x), if you put that into your equation, you can see it will not effect either h or k,

the graph will not be shifted, in this case it is compressed

Answer 38

3*f(x) , if you multiply the entire equation by 3, you see it will affect the a term and the K term,

the graph will be compressed and shifted upwards

Answer 39

f(x) = a(x-h)^2 +k

3*f(x) = 3a(x-h)^2 +3k