Question

alg2

Answer 1

First, I would graph the equation at www.desmos.com/calculator

Answer 2

I dont understand how to graph on that site

Answer 3

okay, hold on

Answer 4

okay

Answer 5

okay ..

Answer 6

now...graph the answer choices and see which one changes the vertex. there is an eaiser way to do this, but for the life of me i cannot remember it

Answer 7

I dont get how to graph it

Answer 8

Okay, let's take the first answer choice
- f(x+4)
This means do this:
-f(x+4) = -[3((x+4)-3)^2]

Answer 9

so graph
\[-(3(x+1)^2)\]

Answer 10

okay

Answer 11

did you graph it? if the graph of that equation has a different vertex than shown earlier, than that is the correct answer choice. If not, then we have to graph more

Answer 12

1,0 vertex?

Answer 13

Oh, I just realized something. I misread the question...

Answer 14

For each function written below you have to describe the change in the vertex (meaning all of them will change the vertex in some way)

Answer 15

You can still graph, but instead of choosing an answer choice, describe how the vertex is moved

Answer 16

if you are asking about
-3(x+1)^2

to match that with
a(x-h)^2 + k
we write x+1 as x- -1 , and add +0
-3 (x - -1)^2 + 0
now we see h= -1 and k=0

Answer 17

yeah i have to figure out how they change

Answer 18

THANK YOU @phi I was trying to come up with a short cut to finding out of the vertex without graphing

Answer 19

but I totally forgot what is was...
vertex = (h,k)

Answer 20

what is the original equation?

Answer 21

Okay, so if the vertex was originally (3,0), and with this equation it is (-1,0), what translation caused the vertex to move?

Answer 22

Basically you are describing the moves down/up and right/left that got it from (3,) to (-1,0)

Answer 23

(3,0) *

Answer 24

so how do i solve for the other one

Answer 25

in a formula method

Answer 26

im not good with the graphs

Answer 27

studygurl was showing how.
(although once you figure it out, you can memorize the rules on how the function is shifted)
for
- f(x+4)
there are two things you changed: you multiplied by -1 and you change x to x+4

Answer 28

in other words, you change
f(x)= 3(x-3)^2+2
to
-3 (x+4 - 3)^2 + 2
which simplifies to
-3 (x- -1)^2 + 2

compare that to
3 (x - 3)^2 + 2

Answer 29

listen to @phi he/she is doing a better job lol. i have to go anyway

Answer 30

do you know what the vertex of the original equation is ?

Answer 31

in other words, match
a (x - h)^2 + k
with
3 (x - 3)^2 + 2

the vertex is at (h,k)

Answer 32

-3 and 2

Answer 33

you should match
x - h
x - 3
h is not -3

Answer 34

yes. next, we find the vertex of the "new version"
-3 (x- -1)^2 + 2

Answer 35

match
x with x
- with -
-1 with h

Answer 36

oops that should be
a (x - h )^2 + k
-3 (x - -1)^2 + 2

Answer 37

It's worth getting the hang of matching these formulas. It will help you.

Answer 38

yeah so the vertex would be postive 1,2

Answer 39

a vertex of 1,2 would come from
a (x - h )^2 + k
-3 (x - 1)^2 + 2

which is different from what we have.

Answer 40

but two - equals to a positive

Answer 41

yes, and that is what we use to rewrite (x+1) as (x - -1)
the reason we want the second way is we want to match with (x - h)
so we look for x. check
look for minus sign. check
look for number.... we see -1
the number is h

Answer 42

I still see the vertex being 1,2

Answer 43

ok. When I get into that way of thinking (that the answer is one way, but I'm told its not)
then I back up and try to figure out what I am thinking that is wrong. (because I'm thinking something that is not true.)

to help figure out what is going on (in your head), you should look at these
-3 (x - -1)^2 + 2 h is -1
-3 (x - 1)^2 + 2 h is 1

Answer 44

okay ..

Answer 45

if you can't figure it out now, think about it later (Lots of times it clicks later)
Meanwhile
the original vertex is (3,2). the new vertex is (-1,2)
which way did we move? and how far? any idea?

Answer 46

left 2 times

Answer 47

?

Answer 48

the y is the same (it's 2) so we do not move up/down
the x changes from 3 to -1
what is the difference between 3 and -1?
to find out we could count. 3,2,1,0,-1 (4 steps to the "left" i.e. towards the minus direction)
or we could subtract 3 - (-1) = 4
either way, we get 4 (and it is to the left)

we started with f(x) and changed to f(x+4) (ignore the minus sign for the moment)
we changed the "x" which is a hint we moved sideways.
the +4 means 4 steps sideways.
the only thing that is confusing is +4 means we moved *left*

Answer 49

btw, if we change f(x) to f(x-4) that would be 4 steps to the *right*
(This is confusing, but that is how it works)

Answer 50

ok so far?

Answer 51

yeah i already turned in the work thanks for helping me