View Full Version : Pre-Calculus (Algebra 3) question


Impromptu_DTour
04-23-10, 11:24 PM
I understand that the term (Math does not = ADD) is not true, and since im not getting this.. i figured "WHY not.. ask on the Forum.", hope this makes sense to someone out there ;)

im about 1/3 the way through this course.. and im doing it online.. and i *laughing* really shouldnt have done it online.. LOL!!

im having an issue with Multiplicities. Its rudimentary stuff i know.. but my issue is not with identifying the Multiplicities and their Occurances..

Nor is it identifying what the behaviors of those occurances of the value of X is..

Its identifying what is the "largest" value of X, vs. the "smallest" value of x

kind of embarassing, as i seem to get the other parts of this concept just fine.. and the part that im not getting doesnt seem to apply directly to the matter at hand at all.. but oh well.. fml i guess. LOL!!

OK. so for instance..

f(x) = 10x^7 - 25x^5 - x^9

i get that i start by factoring out -x^5

f(x) = -x^5 (x^4 -10x^2 + 25)

(though im not sure why that changes the sign infront of the 10 when i rearrange, but ive kind of accepted that it does.. does factoring out the negative sign flip ALL the signs? - anyway .. thats not my main issue.. ONWARD!!)

so ive factored out -x^5

f(x) = -x^5 (x^4 - 10x^2 + 25)

and factor further:

f(x) = -x^5 (x-5)^2 = 0

OK.. so now i have 3 multiplicities of X..

5, 2, and 1.

my issue is decifering which one is the Largest, etc.. i would imagine that 0 would be the largest x-intercept... even if it only has 1 occurrence.. and (x-5) would be the smallest.. (x minus 5... *shrug* makes sense), and has 2 occurrences.. and -x would be the other X.. with 5 occurrences.


Buuutt... im wrong. Why? This becomes an issue for me, because when i need to decide if my graph is just going to cross the x axis .. or if its just going to touch it and turn back.. grrr

its so obtusely obvious im sure.. but Double You Tee Eff people?

=)

I_DTour

Impromptu_DTour
04-23-10, 11:36 PM
i just realized a typo i had up there.. i didnt have a ^2 exponent inside my (x-5)^2 term.. i should have had:

-x^5 (x^2-5)^2 = 0

but i also wasnt doing that in my figuring.. was that my catastrophic error?? would that make (x^2-5) my greatest value for x? followed by 0 then -x?

I_DTour

mildadhd
04-24-10, 12:07 AM
I_DTOUR
I have no idea,
but your post made me realize that I haven't tried math since I started taking AD(H)D medication. I wish I new the rules. I really enjoyed trying to figure out your question. But I think there is some rules I haven't learned in the past, but you've inspired me to look into something mathematical.
I just took 5 weeks off the AD(H)D medication and now I'm really enjoying the focus with the medication.
Take Care.
FH

Pamplemousse
04-25-10, 09:32 AM
Oh boy. Pre-Calc and Calc are honestly the hardest courses I have ever taken. Right now I am 30 weeks into the school year (out of 40 weeks) and I have decided to drop the class because my average is a 45. :eek:

I only understand one thing from the whole entire year. Derivatives. And I don't even fully understand those! I only get the initial step to solving them. BLERG.

I'm the only one in the class with ADD though and I think it's rather odd how I'm the only one failing.

Maybe you can get a tutor or something. Or even buy a book to help you understand. I know there is a book called Calculus for dummies, I think there might be a pre calc one too. Good Luck!

Tarcin
02-02-11, 12:22 AM
Ok I'm in algebra 2 only, but I didn't get your factoring.

If you have:
f(x) = 10x^7 - 25x^5 - x^9
Wouldn't you take out x^5
and get 10x^2-25-x^4
and rearrange it to -x^4+10x^2-25
And I don't think you can simplify it the way you did.

I sort of just zoned out on the rest... sorry

Do what I do with multiplicities... graph :D

I might be wrong though, actually I probably am.
I'm pretty sure taking out -x^5 would make all negatives positive.

hypergirl96
02-02-11, 12:25 AM
f(x) = 10x^7 - 25x^5 - x^9

i get that i start by factoring out -x^5

f(x) = -x^5 (x^4 -10x^2 + 25)

(though im not sure why that changes the sign infront of the 10 when i rearrange, but ive kind of accepted that it does.. does factoring out the negative sign flip ALL the signs? - anyway .. thats not my main issue.. ONWARD!!)

so ive factored out -x^5

f(x) = -x^5 (x^4 - 10x^2 + 25)

and factor further:

f(x) = -x^5 (x-5)^2 = 0

OK.. so now i have 3 multiplicities of X..

5, 2, and 1.

my issue is decifering which one is the Largest, etc.. i would imagine that 0 would be the largest x-intercept... even if it only has 1 occurrence.. and (x-5) would be the smallest.. (x minus 5... *shrug* makes sense), and has 2 occurrences.. and -x would be the other X.. with 5 occurrences.


Buuutt... im wrong. Why? This becomes an issue for me, because when i need to decide if my graph is just going to cross the x axis .. or if its just going to touch it and turn back.. grrr

its so obtusely obvious im sure.. but Double You Tee Eff people?

=)

I_DTour

i dont understand any of that. is that what awaits me in several years? :eek: you have now made me sscared of continuing through high school :eek:

Tarcin
02-02-11, 12:32 AM
Don't worry, it gets easier as you progress. Just listen in algebra!

Bezuidenthustra
02-02-11, 12:39 AM
Don't worry, it gets easier as you progress. Just listen in algebra!

This is correct, hypergirl.

I'll never say this for any other subject, but as a former math tutor, I will say this about math: DON'T SKIP STEPS.

If, at any point, you feel like you don't understand something or you're not keeping up, go get help. Ask your teacher. Ask friends. Ask tutors. Even come on here and ask me. Nowhere are the basic building blocks more important than in math. Each step builds on the previous one. If you missed a step somewhere, it'll force you to miss a concept later on, you'll fall behind completely, and that can spiral out of control very quickly.

Math isn't that difficult or complex if you don't skip the steps and make sure you've got a good grasp on each step before you go on to the next one. If you understand concepts well enough, you'll even be able to teach yourself some of the next steps. That's how important the basic building blocks are. hahaha

This post isn't to scare you. Basically, I'm just saying that if you listen and make sure you understand everything, you'll be fine. And feel free to come and ask me if you don't get it -- if I can't remember what you're struggling with, I come from a family of engineers and physicists who'll quickly be able to tell me the easiest way to explain.

hypergirl96
02-02-11, 12:49 AM
im actually okay ina algebra, the wy my mind works. that is algebra 1. skipping steps is a big issue with me. my parents are both electrical enginers and they try to help me with math, but they dont understand that theyve had many more years of formal education than me and im not at their level. *sight*

thanks for the advice guys. ill reeeeaaaally try and pay attention next year when i start algebra 2.

im still scared for pre-calc though. it looks so complicated!!!!!!!

Icecream
02-02-11, 12:53 AM
Thanks for the aversion therapy. I won't try going there.

Tarcin
02-02-11, 01:05 AM
Naw hyper thats not too hard. Though I'm pretty sure it would look hard if you haven't done exponents yet.

Bezuidenthustra
02-02-11, 01:07 AM
im actually okay ina algebra, the wy my mind works. that is algebra 1. skipping steps is a big issue with me. my parents are both electrical enginers and they try to help me with math, but they dont understand that theyve had many more years of formal education than me and im not at their level. *sight*

thanks for the advice guys. ill reeeeaaaally try and pay attention next year when i start algebra 2.

im still scared for pre-calc though. it looks so complicated!!!!!!!

It isn't. Don't worry.

Want a hint about calculus? It's where you give up neat perfection. If you can grasp that, you'll be fine.

In most other mathematical systems - e.g. algebra - you work with exact equations. If you're doing it right, one side always equals exactly the other side, no matter how you move stuff around. That's the trick with the stuff you're doing right now, and that's the trick next year as well - all your formulas will be there to help make sure you find a way to make one side a mirror of the other, just written a different way. But in calculus, you're working with approximations. Yeah, they're very specific and almost-exact approximations, but they're still approximations.

Here's a way to visualize it. Imagine drawing a circle in Photoshop. It looks like a circle, right? Obviously. But what happens when you zoom in a bunch of times? Each segment looks more and more straight, right? The more pixellated it gets, the closer you get to having a tiny bit of a circle look like a straight line. That's an example of how calculus works. In order to figure out really dynamic stuff, you're going to break it down into very tiny chunks so that something that's super complex is approximately linear, just like a really close zoom of a bit of a circle makes that chunk look approximately straight (you know it's not actually straight, since no part of a circle can ever be straight, right?). Once you break something complex down into something simple, it's a lot easier to figure it out. In math, linear is easy.

Now, in order to be able to make those approximations, you need to acquire some tools. That's what pre-calculus is all about. You'll learn how to take complex algebraic equations apart and how to put them back together again. You'll also learn how trigonometry works and play around with that. (If your teacher's any good, you'll also learn why trigonometry's so important.) All of these things are solid and linear and exact. Then, once you have those basic tools and concepts down, you can use them to do things that are more speculative.

That's calculus. It's speculative. It allows you to predict stuff by approximating a few things and drawing conclusions from your approximations that are so close to true, they may as well be true. You'll be doing a lot of assuming and using the tools you picked up to work those assumptions into balanced equations. But if you always remember that you're dealing with something that's not exact, that that's okay, and that that's the whole point of calculus - to help predict things that are so dynamic they can't be done with simple algebra - you'll be on the right track.

And one last thing: the language is going to sound confusing and daunting, so figure out a way to make it sound simpler. It's really all overcooked. Half the battle is translating the language into something that works in your head. Don't make them feel like you have to be Newton to understand what's being said. hahaha

hypergirl96
02-02-11, 01:08 AM
Naw hyper thats not too hard. Though I'm pretty sure it would look hard if you haven't done exponents yet.

ive done exponents before, but not like those! but thanks for ttryiing to cheer me up :)

Bezuidenthustra
02-02-11, 01:16 AM
ive done exponents before, but not like those! but thanks for ttryiing to cheer me up :)

It's way easier when it's not typed on a computer. All the "^"s are hella distracting. I was super confused when I read through it too. hahaha

Tarcin
02-02-11, 06:59 AM
But watch out for Pascal and his blasted triangle in algebra 2. GOSH

Kingway
02-06-11, 09:16 PM
I understand that the term (Math does not = ADD) is not true, and since im not getting this.. i figured "WHY not.. ask on the Forum.", hope this makes sense to someone out there ;)

im about 1/3 the way through this course.. and im doing it online.. and i *laughing* really shouldnt have done it online.. LOL!!

im having an issue with Multiplicities. Its rudimentary stuff i know.. but my issue is not with identifying the Multiplicities and their Occurances..

Nor is it identifying what the behaviors of those occurances of the value of X is..

Its identifying what is the "largest" value of X, vs. the "smallest" value of x

kind of embarassing, as i seem to get the other parts of this concept just fine.. and the part that im not getting doesnt seem to apply directly to the matter at hand at all.. but oh well.. fml i guess. LOL!!

OK. so for instance..

f(x) = 10x^7 - 25x^5 - x^9

i get that i start by factoring out -x^5

f(x) = -x^5 (x^4 -10x^2 + 25)

(though im not sure why that changes the sign infront of the 10 when i rearrange, but ive kind of accepted that it does.. does factoring out the negative sign flip ALL the signs? - anyway .. thats not my main issue.. ONWARD!!)

so ive factored out -x^5

f(x) = -x^5 (x^4 - 10x^2 + 25)

and factor further:

f(x) = -x^5 (x-5)^2 = 0

OK.. so now i have 3 multiplicities of X..

5, 2, and 1.

my issue is decifering which one is the Largest, etc.. i would imagine that 0 would be the largest x-intercept... even if it only has 1 occurrence.. and (x-5) would be the smallest.. (x minus 5... *shrug* makes sense), and has 2 occurrences.. and -x would be the other X.. with 5 occurrences.


Buuutt... im wrong. Why? This becomes an issue for me, because when i need to decide if my graph is just going to cross the x axis .. or if its just going to touch it and turn back.. grrr

its so obtusely obvious im sure.. but Double You Tee Eff people?

=)

I_DTour

Have u learned the derivatives? If so, use it and look at where F'(X) = 0; this is where the function will change its way (growing/decreasing), and find out the absolute maximum and minimums by comparing the relatives ones. But the derivatives are part of calculus, right? Sorry, I just don't know how it works in english, I learnt that in french.