Absolute Values--beyond the basics question

[Storm Bay]

Dd passed the honours Algebra 1 math test at the local ps yesterday, and scored high enough to make the cut for their honours classes (which are quite good and include theory, etc). She excelled in the open questions and did a great job of showing she understood the process (but got some of the mulitple choice ones wrong for some reason.) She now has to take the Algebra 2 test Monday, since she's been doing that; the woman is trying to decide if dd should start mid-semester or do it next semester.

 

Here's the catch--unlike any of the Algebra 2 texts I've looked at,

which aren't many (Dolciani, Foerster's and something at the library, plus I've looked at Gelfand's) they do their entire second chapter on absolute values, rather than doing bits here & there. Dd understands what that is, but the director of the math dept penciled out an equation unlike any dd has seen and asked her if she'd be able to tell which graph it would make in a multiple choice question.

 

I don't have it, but it started with y=, but then was followed by 3 or 4 absolute values. So far, I've seen nothing like this in the books I checked or on some sites I found last night. I'd hate to see dd have to do start Algebra 2 again when she's done so much of it already because of this--and all of their Algebra 2 apparently hinges on this absolute value class.

 

Does anyone here know of any links that might show this and how to handle it? It may not be that significant since she understands a fair bit, and there may not be enough time, since she is supposed to take this test Monday (only day she can do it next week since there's a PD day for the teacher's Tues, and this woman is observing classes Wed & Thurs--she only teaches on class per day). However, since math is one subject dd works hard in, she'd like to see what she can learn about this before then.

[KAR120C]

Were the absolute values nested? like y=|||x-2|+4|-12| ?

[Luckymama]

Dd15's entire Alg 2 text is online. She's at school right now and I don't know the link, but I'll put it up as soon as I can. She doesn't have a personal code, it's a general access type link.

[Storm Bay]

Were the absolute values nested? like y=|||x-2|+4|-12| ?

 

 

Yes! That's what dd hasn't done and I haven't been able to find.

 

After this I did receive an email listing what is covered in the ps honours math course and it doesn't look like the entire chapter is on this (not sure why I thought that, but it was a long meeting) but this is exactly what dd doesn't know how to do. I'd rather she jump into the Honours Algebra 2 than the Honours Geometry. She will have to redo Geometry because she got stuck on one problem & didn't finish the test, but I'm happy about that because I'm not comfortable with her having done it all on her own. Algebra, yes, but not Geometry with proofs. Plus she'll finally have to do paragraph proofs in the honours course.

 

So, how do we handle this?

Edited October 29, 2010 by Karin

[Storm Bay]

Dd15's entire Alg 2 text is online. She's at school right now and I don't know the link, but I'll put it up as soon as I can. She doesn't have a personal code, it's a general access type link.

 

 

Thanks--that would be great. Even if it doesn't answer this question, it might help with other review.

[KAR120C]

Yes! That's what dd hasn't done and I haven't been able to find.

I only ask because one of my tutoring kids got stuck on that a week ago - apparently it's common!

 

Just for a quick look, I would have her graph a few on a calculator just to see. When you nest them, the standard "v" of the graph can get inverted a few times, making it a zigzag. It can be a turn (pair of turns) for every nested set (although it depends... if you have a + outside an absolute value, that one isn't going to invert it -- it's only if it can go negative again).

 

You can find the turns at the points where each nested set would go be 0. So for the one I gave as an example:

 

y=|||x-2|+4|-12|

 

You'll have a point where x-2=0 (at x=2) for the innermost set... then you check the next set out (can't turn negative because you're adding to an already-positive number) and then the next set out...

|x-2|+4=12

|x-2|=8

x-2=8 or x-2=-8

x=10 or x=-6

 

So you have three points where it turns. If the +4 in the middle was a -4, you could have two more. (Potential to hit zero again!)

 

If she graphs a few on the calculator she can see where pluses and minuses inside the abs() can turn things... experiment a little and see what she gets!

Edited October 29, 2010 by KAR120C

[Storm Bay]

I only ask because one of my tutoring kids got stuck on that a week ago - apparently it's common!

 

Just for a quick look, I would have her graph a few on a calculator just to see. When you nest them, the standard "v" of the graph can get inverted a few times, making it a zigzag. It can be a turn (pair of turns) for every nested set (although it depends... if you have a + outside an absolute value, that one isn't going to invert it -- it's only if it can go negative again).

 

You can find the turns at the points where each nested set would go be 0. So for the one I gave as an example:

 

y=|||x-2|+4|-12|

 

You'll have a point where x-2=0 (at x=2) for the innermost set... then you check the next set out (can't turn negative because you're adding to an already-positive number) and then the next set out...

|x-2|+4=12

|x-2|=8

x-2=8 or x-2=-8

x=10 or x=-6

 

So you have three points where it turns. If the +4 in the middle was a -4, you could have two more. (Potential to hit zero again!)

 

If she graphs a few on the calculator she can see where pluses and minuses inside the abs() can turn things... experiment a little and see what she gets!

 

Aha, we need a graphing calculator for this? We don't have a graphing calculator. Is there a way to do this with a regular scientific calculator or by hand?

[KAR120C]

Aha, we need a graphing calculator for this? We don't have a graphing calculator. Is there a way to do this with a regular scientific calculator or by hand?

It just takes longer! The only reason I mentioned the graphing calculator is that you can throw in three or four different variations on one equation quickly and see what changes about the graph, without taking the time to do it by hand. The process and the graph are the same either way of course!

[Kathy in Richmond]

Karin - Here's a free online graphing calculator you can use. I tried out the sample equation you've been working on & it worked. Just use abs(abs(abs(x-2) +4) -12) as your input. You may need to use the zoom out function to see the whole picture.

 

~Kathy

[Storm Bay]

Karin - Here's a free online graphing calculator you can use. I tried out the sample equation you've been working on & it worked. Just use abs(abs(abs(x-2) +4) -12) as your input. You may need to use the zoom out function to see the whole picture.

 

~Kathy

 

Thanks!