Absolute Value Function or Parabola?

[Jason76]

\(\displaystyle x^{2} - 6x + 9 = (x - 3)^{2}\)

The book says it's should be graphed as an absolute value function.

Domain would be all real numbers.

Range would be 0 toward + infinity.

Why?

 

[Deleted member 4993]

\(\displaystyle x^{2} - 6x + 9 = (x - 3)^{2}\)

The book says it's should be graphed as an absolute value function.

Domain would be all real numbers. How do you interpret this statement?

Range would be 0 toward + infinity. How do you interpret this statement?

Why?

I don't know why y = (x-3)² should be graphed as y = |x-3|. Those two are similar functions - but not the same. To see the similarity - and dissimilarity - plot those two functions on the same screen and observe!

 

[Bob Brown MSEE]

This is a very strange problem.
I suspect that it was worded incorrectly when you got it, Jason.

This problem is more interesting worded this way
[FONT=MathJax_Main]y = ( | [/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main] | [/FONT][FONT=MathJax_Main]− [/FONT][FONT=MathJax_Main]3 [/FONT][FONT=MathJax_Main])[/FONT]^{[FONT=MathJax_Main]2[/FONT]}

Range would be 0 toward + infinity.
Domain would be 0 toward + infinity.
Why?

 

[HallsofIvy]

.
Or \(\displaystyle y= \sqrt{x^2- 6x+ 9}= |x- 3|\)

 

[wjm11]

\(\displaystyle x^{2} - 6x + 9 = (x - 3)^{2}\)

The book says it's should be graphed as an absolute value function.

Domain would be all real numbers.

Range would be 0 toward + infinity.

Why?

The point is that the right hand side of the equation is "something squared" and therefore must always be positive. However, I strongly suspect you have not posted the original problem in its entirety. Please do so if that is the case.

 

[Bob Brown MSEE]

The point is that the right hand side of the equation is "something squared" and therefore must always be positive. However, I strongly suspect you have not posted the original problem in its entirety. Please do so if that is the case.

I believe Halls has the correct read.
This problem is posted correctly!

 

[Deleted member 4993]

I also think HoI "guessed" the problem correctly. However, in that case the problem was not posted correctly. It should have been posted as:

y² = (x-3)²

In his title the OP put "parabola" - which indicated to me that the LHS was y¹.

 

[Jason76]

The original problem was on this page.

http://www.analyzemath.com/Graphing/graphing_square_root_func.html

 

[Deleted member 4993]

The original problem was:

[SIZE=-0]f( x ) = SQRT (x ² - 6x + 9)

As suspected, the original-posting was incorrect (and incomplete).[/SIZE]

 

[Bob Brown MSEE]

Let us use write the expression under the square root as a square as follows <=== very important
\(\displaystyle x^{2} - 6x + 9 = (x - 3)^{2}\)

The book says it's should be graphed as an absolute value function.

Domain would be all real numbers.

Range would be 0 toward + infinity.

Why?

Hi Jason,

You did express your problem correctly, it had to do with the way that you read the published problem.
You had not seen the sentence in blue as part of the expression. (see quote at top of this reply)
I don't blame you, the sentence is VERY POORLY WORDED.
However, If you had simply given us the link, I would not have understood your issue.

This is why we like people to express the problem in their own words (show their work, as you did).
However next time, also include the exact wording or a link if you have it.
In fact, include all information like hints from teacher or answer in back of your book

I don't believe that we have answered your question. -- sorry.

The answer is that:
You had not seen the sentence in blue as part of the expression.
you are correct that, the expression is a parabola. (as you wrote it)
however, the expression is like an absolute value function. (after you "write the expression under the square root")

This is a very interesting post! A person might not guess that a parabola may change to an absolute value function by simply taking the square root. Cool!

 

[mmm4444bot]

Okay, Jason. It's time for us to have our little conversation again.

There is a reason why these boards have posting guidelines.

When people do not understand what they are doing, they waste a lot of their time. Our posting guidelines are designed to help prevent you from wasting your time.


In future requests for help, please provide us with all of the information that you have. Do this as soon as you start a thread.


You do not yet have sufficient understanding to take shortcuts. You also have difficulty with misstating information. You may be working with poor material.

Additionally, I have reviewed your posts, and I see a pattern of skipping information that we post for you OR skipping direct questions that we ask of you.

If you do not understand something, please say so. We can always rephrase or elaborate on our instructions, or we can explain our questions for you. When students skip over things in front of them that they do not understand, the learning barriers grow taller. You will eventually need to revisit these issues, anyway. Putting them off iincreases your workload and wastes your time!

I hope that this is clear, now. Do not keep information secret, when you're asking for help. Ask specific questions. If you continue to fail our guidelines, I may put your postings on moderated status; this means that your posts will not appear on the board until after a moderator has reviewed them, which could take hours.

:idea: Is that web site "the book" that you keep referencing? You may want to consider a better "book" because I noticed some questionable statements at that site.

 

[Deleted member 4993]

Hi Jason,


you are correct that, the expression is a parabola. (as you wrote it)
root. Cool!

No it is not ..... it is a part of a degenerated hyperbola [ y² - (x-3)² = 0] - another conic section

also known as pair of straight-lines [y = ± (x-3)]

 

[Jason76]

Okay, Jason. It's time for us to have our little conversation again.

There is a reason why these boards have posting guidelines.

When people do not understand what they are doing, they waste a lot of their time. Our posting guidelines are designed to help prevent you from wasting your time.


In future requests for help, please provide us with all of the information that you have. Do this as soon as you start a thread.


You do not yet have sufficient understanding to take shortcuts. You also have difficulty with misstating information. You may be working with poor material.

Additionally, I have reviewed your posts, and I see a pattern of skipping information that we post for you OR skipping direct questions that we ask of you.

If you do not understand something, please say so. We can always rephrase or elaborate on our instructions, or we can explain our questions for you. When students skip over things in front of them that they do not understand, the learning barriers grow taller. You will eventually need to revisit these issues, anyway. Putting them off iincreases your workload and wastes your time!

I hope that this is clear, now. Do not keep information secret, when you're asking for help. Ask specific questions. If you continue to fail our guidelines, I may put your postings on moderated status; this means that your posts will not appear on the board until after a moderator has reviewed them, which could take hours.

:idea: Is that web site "the book" that you keep referencing? You may want to consider a better "book" because I noticed some questionable statements at that site.

Sorry, from now on I will post the web source of my examples. Some of the websites I used had wrong answers, but one wrong equation came from "Barrons - Pre-Calculus Made Easy" Book (otherwise a good book). Anyhow, I will try to look for better books, as well as answer questions from other forum posters more promptly.