Question

Help with two algebra questions please?
What is the graph of the absolute value equation?
y=|x| -9

Answer 1

I'd start by graphing just y = |x|.
Then, because of the " -9 " I'd translate the entire graph downward 9 units.

That's it. Can you now choose the correct answer?

Was there another problem you'd wanted to discuss?

Answer 2

answer is 4

Answer 3

Just a reminder: the shape of the absolute value function is like that of a " V " with vertex at (0,0).

Answer 4

answer is 4 again

Answer 5

I meant, "the shape OF THE GRAPH of the absolute value function ... "

Answer 6

Thank you both!
I know I said two but one more?

Answer 7

The graph of y = |x+4| looks like that of y = |x|, except that ... what? Can you finish this description?

Answer 8

Hope you won't mind, but I'd like for you to answer that question before we do #3.

Answer 9

its up by 4 units

Answer 10

Beth, please hold that for a moment.

nkaadi: Please justify your answer (immediately above).

Answer 11

I'd like for nkaadi to justify HER answer. You and I can come back to that question after we've heard from her/him.

Now regarding the newest question:


y = |x+3|-4,

Answer 12

Please start with the graph of y = |x|, as before. Which 2 changes would you make to this graph to obtain the graph of y = |x+3| - 4 ?

Answer 13

answer is 2 not 4

Answer 14

what should i verify math male

Answer 15

i just verified with x=0, and x=1

Answer 16

no for the third question it is 2

Answer 17

mathmale which graph should i verify

Answer 18

i am male my name is aadithya from india

Answer 19

It'd make more sense for me, for Beth and perhaps for yourself if you'd please show your work (describe the steps you've taken) instead of saying "it's 2, it's 4, and so on. I asked you to explain how you decided, several minutes ago, that "its up by 4" in response to y = |x+4|.

Answer 20

put x=0,you get y=4 easy

Answer 21

aadithya: welcome to Open Study, and thank you for contributing. could you please try to justify your answer, above? I'll repeat the info I gave you if you wish.

Beth:

Answer 22

Beth: how would you graph y = |x+4|?

Answer 23

first y=modx then shift the graph upwards by 4 units

Answer 24

Beth, I won't say more until we've heard from you. Your turn.

Answer 25

what is your answer mathmale

Answer 26

aadithya: Since it was Beth who initially posted questions here, I feel that she deserves first priority, and again invite her to answer.

After she does, you and I, or you, Beth and I, could continue with your own questions and suggestions. I value your participation, but right here and now it's Beth's game.

Answer 27

Beth, I was asking you how you would graph y = |x+4|. Ignore the 3 for now.

Answer 28

i have to go now guys should prepare for exams
cya all the best beth and mathmale
take care

Answer 29

Hope to see you back on OpenStudy again soon! Best to you, too. Bye!

Beth?

Answer 30

Beth, sorry, but I have to counter that.
If y ou start with y = |x|, you get a v-shaped graph with vertex at (0,0), right?
if you then want to graph y = |x| + 3, you move the whole graph of y = |x| upward 3 units.

y = |x+4| is quite different. Its y-intercept is 4, yes. But where is its vertex?

Answer 31

And I'd like for you to describe what you do with the graph of y = |x| so that it becomes the graph of y = |x+4|. This is quite important. It's called "horizontal translation." What does that mean?

Answer 32

math male are you there

Answer 33

surely am. Please, aadithya, post your questions, one at a time, in the usual way. (Start a new problem, rather than adding a problem to a previous discussion.)

Answer 34

ya about the graph question
is my answer wrong

Answer 35

Regarding y = |x| + 4: we just translate the graph of y = |x| upward 4 units.
Regarding y = |x+4| = |x - (-4)| is quite a different situation. Please try again on this problem.

Answer 36

ok i think you are right

Answer 37

Again I invite y ou to explain what you would do to the graph of y = |x| to end up with the graph of y = |x+4|.

Answer 38

yep you are right i was wrong i just verifired the graph
you in college??

Answer 39

for y=modx+4 the vertex is at (-4,0)

Answer 40

thanks a lot can you tell beth

Answer 41

that's great. True.
What I hoped you would say was, "to obtain the graph of y = |x+4| from the graph of y = |x|, we simply shift the whole graph of y = |x| four units to the left.

Answer 42

ya

Answer 43

answer to 3rd question is 2 i guess

Answer 44

OK. Now, start with the graph of y = |x|. What do you have to do with it to obtain the graph of y = |x+4|-2?

Answer 45

Draw this new graph. Use the Draw utility (below).

Answer 46

same thing shift the graph left by 4 and then down by 2

Answer 47

that's exactly right. Congratulations!

Answer 48

the vertex is(-4,2)

Answer 49

do you live in india

Answer 50

tell beth about the corrections thanks

Answer 51

soryy its (-4,-2)

Answer 52

No, but I'm quite interested in India. I live in Southern California, about three hours by car from Los Angeles. Where do you live?

Answer 53

in banglore india are you in college

Answer 54

I was in college full-time for 5 years, part-time (graduate study) 4.5 years, and taught deaf students Math in New York State 43 years. I've just retired and now live in California.

Answer 55

great i am a 12 grade student in india

Answer 56

i respect you sir

Answer 57

thank you, aadithya. I'm truly glad to be in touch with you and hope you'll post further problems here on Open Study as time goes by.

Answer 58

love to visit usa one day sir and thanks

Answer 59

And I'd love to visit India. All the best to you; hope we'll talk again. Take care! Bye for now.

Answer 60

see you again bye