Question

Given the function f(x) = 4(x + 1)2 - 3, indicate the shifts that will affect the location of the vertex, and explain what effect they will have. Use complete sentences.

f(x-2)
f(x) - 2
f(2x)
2*f(x)

Answer 1

@calculusfunctions

Answer 2

explain please

Answer 3

@1017squad do you want @DanJS to just do the work for you and give you the answers or do you want someone to teach you? As a teacher I'm here to teach. It is very unsettling to see everyone simply showing off and just giving out the solutions. How is one supposed to learn?!

Answer 4

well to be honest im not really trying to learn this but it wont hurt and i understand what your saying

Answer 5

@calculusfunctions i need an explanation on why these work so id rather learn it

Answer 6

OK then, given a quadratic function in vertex form\[y =a(x -p)^{^{2}}+q\]If a > 1 then the parent function is vertically stretched by a factor of a,
If a < 1 then the parent function is vertically compressed by a factor of a,

If p < 0 (x + p) then the parent function is shifted p units left,
If p > 0 (x - p) then the parent function is shifted p units right,

If q < 0 then the parent function is shifted q units down,
If q > 0 then the parent function is shifted q units up

The parent function referred to above is\[f(x) =x ^{2}\]

Answer 7

im honestly lost do you think you can draw it out?

Answer 8

Can you make the connections? In your question, do know a, p, and q?

Answer 9

no sir

Answer 10

Also one thing I forgot to add. If a < 0 (a is negative), then the parabola's direction of opening is downward.

Answer 11

ok i still dont get it

Answer 12

OK so you have\[y =4(x +1)^{2}-3\]and in general\[y =a(x -p)^{2}+q\]Do you not see what a, p, and q values are in your question?

Answer 13

i see it in the question now

Answer 14

ok so whats next

Answer 15

So a = ?, p = ? and q = ? First tell me these values.

Answer 16

i see the numbers but how do i get the values

Answer 17

What do you mean? The corresponding numbers are the values.

Answer 18

so they are 4,1,and 3

Answer 19

Almost!

a = 4
p = -1
q = -3

Do you see that?

Answer 20

Now identify the transformations based on the description I gave you for each parameter.

Answer 21

compressed, shifted to the right and down?

Answer 22

i mean left

Answer 23

For example, if we had\[y =5(x +2)^{2}+7\]Then

a = 5 indicates a vertical stretch (since a > 0) by a factor of 5,
p = -2 indicates a shift of 2 units left (because p < 0),
q = 7 indicates a shift of 7 units up (since q > 0)

Answer 24

so how do i apply this to my problem?

Answer 25

Exactly the same way using your values of a, p, and q and the explanation I gave you.

Answer 26

First you have a = 4, correct? Then from the notes I gave you, what does it mean?

Answer 27

so i do that to get one or two of those 4 choices?

Answer 28

yes it means the parent function is vertically compressed

Answer 29

No, a = 4 > 1, which means it is vertically STRETCHED by a factor of 4. You're not even paying attention!! I didn't write a lesson for my own amusement!

Answer 30

sorry ok so whats next?

Answer 31

Now you have p = -1. Please read carefully about what I said about p and write your answer.

Answer 32

then the parent function is shifted p units left,

Answer 33

Yes but in your question that would be 1 unit to the left. Now finally what about q?

Answer 34

then the parent function is shifted q units down

Answer 35

-3 units down right

Answer 36

YES!

Answer 37

Do you get it now? I would probably save those notes if I were you, for future reference.

Answer 38

Alright then Good Luck!!! I'll be signing out for now.

Answer 39

no one more question please you could just give me an aswer and an explanation