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lisamariewillbe

Quadratic formula

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Well, IMO (as a teacher for 35 years) your problem is right there. If you treat mathematics as memorizing formulae you will never get very far because there's just too much to memorize. If you try instead to understand the basic principles, everything builds on them in a logical fashion and you don't have to remember so much.



IMO (as someone who was a student for 17 years), most teachers unfortunately do not put this emphasis on fundamentals. And let's be practical: if she tried to derive the quadratic formula on an exam, every time she needed it, she'd run out of time.

I am all about the fundamentals, but there is nothing unreasonable about committing the quadratic formula to memory.
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I didn't really get it until I worked it out for myself. Start with your basic trinomial and solve it by completing the square. You know that works, right? Solve that and *poof* you have the quadratic formula. Once I did that I understood and had faith in it and it made a lot more sense.

Good luck. Cheers!

Blue skies and happy landings!

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What other half? Factoring it out? Here's my 2 cents, hope it doesn't confuse you further.

You know FOIL (First Outer Inner Last) right? FOIL is basically reverse factoring. Generating your quadratic when you already have the solution. Here I'll use x=-2 and x=-7/2. I know, looks nasty but negative solutions give you an easier quadratic, which is good here.

(x+2)(2x+7) FOILs out to:
2x^2 + 7x + 4x + 14
Two center terms (O and I) can be combined by adding their coefficients (+7 and +4).
2x^2 + 11x + 14

Assuming you don't already have your solutions (x = -2 and x = -7/2) and you need to solve from the quadratic form, you have your ABC to plug into the quadratic formula (not my method of choice) or you can factor it out.

When factoring a quadratic, you only have so many options. If it doesn't jump out at me, I list a few options and hope it becomes obvious. The easy way (for me) is to focus on only the outside terms and hope the middle term falls into place.

For 2x^2 + 11x + 14:
(2x + 14)(x + 1) yields 2x^2 + 2x + 14x + 14 or 2x^2 + 16x + 14
I realize at this point that no combination of 2, 14 and 1 will give me 11. 2 for the leading coefficient should be self explanatory
(2x + 2)(x + 7) yields 2x^2 + 14x +2x + 14, also 2x^2 + 16x + 14
(2x + 7)(x + 2) works

You'll very soon run into equations where you really can't use the quadratic formula, such as those with more than one variable. Personally the only times I ever used the QF is when it was specifically requested. I think I failed the QF portion of my exams (10+ years ago).

Feel free to PM for more if this helped you out :)

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I'm in agreement with The111 on this. There are a lot of things that are nifty to derive, but sometimes memorization is the way to go.

Think about how many times you've used the half angle trig identities or certain integrals. You derive them once or run through their proof, but in the end, you memorize it and then apply it. Not everybody has to take Real Analysis.

:)
Vinny the Anvil
Post Traumatic Didn't Make The Lakers Syndrome is REAL
JACKASS POWER!!!!!!

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x = -b +/- sqrt((b^2 - 4ac)/2a)

Wait...what was it you wanted to know?



How about x = (-b + sqrt(b^2 - 4ac))/2a and x = (-b - sqrt(b^2 - 4ac))/2a ?

I know it seems like nit picking, but the difference is very important. :)
Math tutoring available. Only $6! per hour! First lesson: Factorials!

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Feel free to PM for more if this helped you out


:S

I have an exam tonight in my algebra class...I am not going to read any more of this thread before I go cross-eyed....:P:S;)

Ciels-
Michele


~Do Angels keep the dreams we seek
While our hearts lie bleeding?~

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but the difference is very important.



That was my problem, I was using only one, either or.... not both. I still hate it but give me 20 mins and I can get it right. :D

Plus he fixed my factoring and Im actually having fun with it but still not perfect but oh well..... *happy dance* I owe Vinny a hug.... from what I hear he will need a step stool though :D

Thanks Vinny ,...... thank you thank you ....

Im sure as soon as I get there to test Ill go brain dead and not be able to remember anything. I love any kind of test besides Math....
Sudsy Fist: i don't think i'd ever say this
Sudsy Fist: but you're looking damn sudsydoable in this

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Next 2 lessons will be Integration by Parts and Differential Equations.




>:(>:(>:( Ill kick your booty......



LOL!! Seriously, I hope the example helped. It's kinda tough to do that over the internet.

You'll do fine on your test. For me, algebra was one of those things that I banged my head against the wall trying to understand, then all the sudden it clicked. The resulting laughter scared the shit out of my mom. :D:D

Again, best of luck to you!!

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but the difference is very important.



That was my problem, I was using only one, either or.... not both. I still hate it but give me 20 mins and I can get it right. :D



Both parts were present; they were just written incorrectly. I won't point out what made them correct, as I don't want to confuse you as you study for your test.

Good luck! :)
Math tutoring available. Only $6! per hour! First lesson: Factorials!

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I haven't had the time to read EVERY post here but it seems that some people are having problems with Quadratic Equations. I'm flattered that some folks have referenced 1 of my calculators www.1728.com/quadratc.htm . (Incidentally, in high school I just got B's and C's in math).
Without confusing the issue too much, there are 3 ways to solve quadratic equations:
• Factoring
• Completing the square
• The Quadratic Formula
You only have to know one method (unless you have a teacher that wants you to demonstrate your skill at using the other 2).
Anyway, the method I always chose was ... you guessed it ... the Quadratic Formula.
If you visit another one of my website's pages:
http://www.1728.com/minmax.htm
you will see what quadratic equations look like when graphed. When you are solving a quadratic equation (or ANY equation for that matter) you are determining at what point(s) the equation equals zero (or at what point(s) the graph of the equation crosses the 'X' axis.)
I figure I've explained enough for now. If anyone wants to reply to this posting please do.
Someone liked the way I explained the derivation of the quadratic formula. Thanks. Yes, I believe mathematics should be explained in plain English.
Ever visit that guy Eric Weisenstein's Mathworld website? Great in depth explanations of mathematical concepts - IF you already have an advanced mathematics PhD with honors. As I said, I like to speak plain English.

[email protected]

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Well, IMO (as a teacher for 35 years) your problem is right there. If you treat mathematics as memorizing formulae you will never get very far because there's just too much to memorize. If you try instead to understand the basic principles, everything builds on them in a logical fashion and you don't have to remember so much.



I do not agree completely. I'm finishing up my undergrad; I've taken all the Diff-EQ, Complex, and Boundary Value Problems mumbo jumbo, and I just don't understand why you have to memorize so much. True, I think memorizing fundementals like the quadratic, unit circle, and a few handy rules for derivative/integrals and such will prove useful in later math courses. I don't think there is a problem with memorizing a fundemental equation like the quadratic. If we had to derive something like a quadratic, or even trig differentials every time during an exam, we would take a lot longer than a 50 minute class period to take the exam. As long as you have seen it and understand where it comes from and know how to apply it, then use it and move on, but remember that to apply it to the next level of math you choose to pursue.

As for memorization-- fundementals like this should be memorized, but IMO, when you get to higher math or higher math that you use inside an enginnering class, you should be able to have any equation needed for reference given to you. I waste more time remembering formulas and equations then I do knowing how to apply them and knowing how to apply them to real life things I might see in my field. When it all comes down to it, when I have my grown up job (as I like to call it;)), I will always have a book on my desk to get the equations I need out of it to use for whatever I'm doing in my field. My employer is not going to care if I can remember more equations than anybody else on the planet, but if I have not a clue in hell on how to apply them, then I'm screwed.

LisaM... best advice is to make friends with another person in class and do the homework together. It takes me a while to get things in my maths, so I make sure to get my butt in the prof's office once or twice a week and to get that study buddy who will be there to help ya out. It's gotten me through math hell for that past four years.

Sorry for the rant, but this gets under my skin when it comes to math-- at least in my case.
Apologies for the spelling (and grammar).... I got a B.S, not a B.A. :)

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Well, IMO (as a teacher for 35 years) your problem is right there. If you treat mathematics as memorizing formulae you will never get very far because there's just too much to memorize. If you try instead to understand the basic principles, everything builds on them in a logical fashion and you don't have to remember so much.


I don't think there is a problem with memorizing a fundemental equation like the quadratic. If we had to derive something like a quadratic, or even trig differentials every time during an exam, we would take a lot longer than a 50 minute class period to take the exam. As long as you have seen it and understand where it comes from and know how to apply it, then use it and move on, but remember that to apply it to the next level of math you choose to pursue.



"Fundamental" and "Basic" are rather subjective terms. :P The few cases where I've helped people with algebra recently have reminded me of this. It would seem that the further you go down the "rabbit hole," the more you start to take for granted.

As for a kind of hidden beauty in the world of mathematics, I think there's some truth to that. I have on my bookshelf at work (amongst others) an Electromagnetics text and an Acoustics text. While at first glance they seem to cover drastically different material, the more you understand each of them, the more you develop an appreciation for just how similar they are. Further down that same avenue, you start to realize it's not just how waveguides and loudspeakers work, it's how just about everything works.

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Hey, Baby! Can you solve a second order non-linear non-homogenous PDE with non-constant coefficients?

Try that as a pick up line in a bar!

Bwaaaahahahahahahahahahaaaaaaa!

Ahhhh tequila...I enjoy thee so...I am all of a sudden motivated to sing Jingle Bells...I wonder if my neighbor ever got in the Christmas spirit...

:P
Vinny the Anvil
Post Traumatic Didn't Make The Lakers Syndrome is REAL
JACKASS POWER!!!!!!

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b/c I'm such a bad, bad catholic boy, I decided to read this entire post as penance.

christ on crutches do i hate math. :S

LM and michele, i don't envy you in the least. i love stats though, go figure... i had a few years of basic and upper level stats in undergrad and graduate school... i could wrap my mind around ANOVA, MANOVA, chi-squares, basic t-tests and all that... maybe b/c it was backed up w/ real examples... drug x was better than placebo on measures x, y, and z, all statistically significant, w/ a p value of.......

I loved that stuff... but this quadratic craziness, sheesh.

I miss Lee.
And JP.
And Chris. And...

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i could wrap my mind around ANOVA, MANOVA, chi-squares, basic t-tests and all that... maybe b/c it was backed up w/ real examples... drug x was better than placebo on measures x, y, and z, all statistically significant, w/ a p value of.



Dude watch it, test in less then 24 hours and your adding terms that with my luck will pop into my head and Ill be in the room thinking wtf do I do while staring at problems Ive been doing over and over and over again ....


BTW MICHELLE.... Howd you feel about how you did on your test?
Sudsy Fist: i don't think i'd ever say this
Sudsy Fist: but you're looking damn sudsydoable in this

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test in less then 24 hours



Sometimes when you think you don't understand the material you actually know more than you think you do. Try not to allow fear of math exams to become a bigger enemy than math. Exam anxiety has done more harm to me in the past than lack of knowledge.


Wishing you the best of luck.

Cheers:)
Richards
My biggest handicap is that sometimes the hole in the front of my head operates a tad bit faster than the grey matter contained within.

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BTW MICHELLE.... Howd you feel about how you did on your test?


Well, let's say I didn't die, but I'm not in heaven, either.

It was only a 9 problem exam...and I know I blew an entire problem; I could feel my brain just stop thinking, stop making sense. And the numbers appeared to be in cuneiform, a language I don't speak or read. Sigh...

But I also know I got all of the bonus questions - 8 points there. They were easy (for me) factoring and graphing, so that will help me enormously. I think I passed, and may have gotten a B. But any more than that is my professor being generous.

I will say the last two quizzes were returned tonight, and out of the whole class, only 5 of us got all available points - 20 in all. So I got the 20, and that gave me a bit of a boost starting the exam.

LM, I pm'd you some of my tricks, and maybe they will help you. I know they help calm my poor little math deficient head, so perhaps they will come in handy for you.

And I've got to add, my professor is a really, really wonderful teacher and lady. She is so encouraging and so understanding...she lets me re-write the test onto the same lined paper I do my homework on so I don't have this big "EXAM" blaring at me with typed numbers and stuff scaring me. As long as I turn it in with my exam paper, she allows me to do this. Somehow, it helps my head to remember the homework problems when I do it that way...but if I'm faced with stark white paper my brain explodes.

My prof is really, really cool. Any lack of understanding the subject matter is not her fault whatsoever; it's just my poor, old, tired, blown brain...

Michael, I think I'll like stats more, too...and primarily because it does deal with real world immediate application stuff, like drugs, profit and loss, et cetera. I've always had a hard time understanding the abstract concepts; if one can show me how it applies, it sticks like glue...which is why word problems aren't too bad for me. I can visualize what I'm trying to get to, and understand why it's important to find the length of board A...you know?

Anyway, it's about 10 days til my next math test...and I've got a huge Anatomy exam next week, as well as a paper to write for Bio this week...so while there's no math right now, I've got plenty else to study for...

Good luck tomorrow, LisaMarie. You'll be fine...and remember, you only have to pass. You don't have to be perfect, just pass.

Ciels-
Michele


~Do Angels keep the dreams we seek
While our hearts lie bleeding?~

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