How to use the quadratic formula | Polynomial and rational functions | Algebra II

How to use the quadratic formula | Polynomial and rational functions | Algebra II | Khan Academy

Рет қаралды 1,996,670

14 жыл бұрын

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Introduction to using the quadratic formula.
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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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Пікірлер: 681

@AAwesomePantss 10 жыл бұрын

I learn more from you than my math teacher

@armo619 10 жыл бұрын

***** IKR

@JustmeAthena123 10 жыл бұрын

I thought I was the only one... hahahaha

@Tony1035610 10 жыл бұрын

JustmeAthena123 xd, my teacher was pretty good, she was more helpful than this, this is just for reference since i forgot/ i have to finish my honors summer packet

@carlbeaston324 9 жыл бұрын

you have a shit math teacher then

@domtoretto1688 7 жыл бұрын

Carol Nguyen lol my math teacher showed me the video

@katsudonewithyoass8359 4 жыл бұрын

Throughout the years this channel has saved my butt so many times. I hope whoever makes these videos is living a prosperous and happy life 😌

@demxnia6736 4 жыл бұрын

Its Sal Khan, he's the founder and CEO of Khan Academy. So yeah, he's living a pretty good life.

@Goosiepoo 3 жыл бұрын

@@demxnia6736 CEO of a non profit

@p2scy 3 жыл бұрын

@@Goosiepoo Sal Khan's net worth is 220 million, so I would say he's living a pretty prosperous life

@rachelt.7123 3 жыл бұрын

at first I thought you said 'preposterous' and got kinda worried for a sec...

@seanli2578 Жыл бұрын

He's graduated from MIT AND from Harvard Business School. His net worth right now is 260 million, so yeah; he's prosperous.

@henrywiley22 6 жыл бұрын

In class we spend weeks on a subject. I just learned what I needed to in 15 minutes for my test tomorrow

@AceOlympuss 4 жыл бұрын

TallishOak are these 3 different equations? I dont understand this

@Derpysquid1730 4 жыл бұрын

yo same

@manface4318 2 жыл бұрын

@Deadlock T so whats the score?

@evil778 2 жыл бұрын

This is one of the many, MANY, reasons why public school is trash.

@iconsumekneecaps 5 жыл бұрын

Who else is staying up at 1 AM watching this and trying to get your homework done in a panic??? 😂

@Murcielag0scuro 4 жыл бұрын

Use photomath. It does it for you and shoes the work. It doesn't work with geometry though, but algebra works.

@ethanisnothere1375 4 жыл бұрын

I don't know, they're reallying pushing you to get the premium

@godlybunniarts8549 4 жыл бұрын

omg its 1:02am and that's exactly what im doing

@mosedali9858 4 жыл бұрын

Lol that’s exactly what I’m doing

@realta9477 4 жыл бұрын

i feel attacked

@blickbeared1064 7 жыл бұрын

Sir I believe that you may have saved my grades, you indirectly told me what I was doing wrong.

@manojkumarroy5337 7 жыл бұрын

blick beared same here bud

@abelalvarado6809 5 жыл бұрын

Students: Can we learn how to do taxes? The Education System: Screams in quadratic formula

@Speeplonk 4 жыл бұрын

Me: spends an hour max on Google "Hey, that was easy!"

@dividale2821 4 жыл бұрын

This is actually fairly useful in lots of fields, like engineering and even programming. We do have computers do some of it for us, but it's still useful to learn this. That said, the education system is for you to prove that you are able to learn advanced concepts, not for you to actually remember all of it.

@abelalvarado6809 4 жыл бұрын

Levon Aronian Yes, it can be useful I understand that, but statistically speaking most people learning this won't use it, wasting a lot of time that we could have used to learn better things

@saturn6305 3 жыл бұрын

Abel Alvarado well u always have ur free time to learn other things

@abelalvarado6809 3 жыл бұрын

@@saturn6305 Yeah but you better believe I'm not gonna waste my time with something I don't have the desire nor need to learn

@diluted_potato8774 8 жыл бұрын

You're amazing, before this I didn't understand quadratics one bit. Thank you so much!

@zanstanium6740 5 жыл бұрын

well, I feel sorry for you now. Your going to pretty much fail your finals.

@tarnished_knight_ 5 жыл бұрын

*spongebob* one million years later . . . .

@sauce1187 4 жыл бұрын

@@zanstanium6740 wait why

@C4RSBERaif 7 жыл бұрын

For the second example, I spent like 15 minutes trying to figure out why my calculator was saying math error until I watched the rest of the video and it doesn't have a real solution....

@evelyncorrea680 4 жыл бұрын

Raif Mas 😂

@benr3799 2 жыл бұрын

I want to be a math teacher, but I needed this refresher. I always mess up the formula because I didn’t learn it by heart. I imagine 99% of people struggling in math just are missing some basic building block like this, and I’m part of that 99%. Thank you again for making math less mysterious and clearly wonderful. I’m arguably more proud of my energy points score than any other academic accomplishment in my life lol.

@junyang1205 3 жыл бұрын

This teaches you more than a zoom meeting ever will

@onikabogdan811 8 жыл бұрын

I've watched about a million of your videos because I came into Algebra in the middle of the semester and now I have the EOCs and I was freaking out that I didn't know any of it. THANK YOU THANK YOU THANK YOU.. I have been saved and now I don't have to worry about failing 8th grade!!!

@shawngerard9327 6 жыл бұрын

Onika Bogdan Ik I’m kinda late but is the eoc hard???

@olympias1528 6 жыл бұрын

Lmao, failing grade 8. You can't fail grade 8. Late ik

@Thatoneguy-ub8xg 5 жыл бұрын

Onika Bogdan so your only a year above me how’s sophomore year?

@benrupert4366 5 жыл бұрын

yo you're now a sophomore

@mx.litzix9100 5 жыл бұрын

@@olympias1528 you literally can.. I know 4 people who got held back in 8th grade

@kappaisreal4399 7 жыл бұрын

At 8th grade (where I am right now),I have been studying hard in school and at Math. I challenged myself to get at least 85%/100% of the answers when having a test without watching some tutorials and it strucked me that I can do it without any help of others I want you to believe in yourself,you can be great by studying hard and please do not let your guard down

@fearr3951 2 жыл бұрын

Hows college mate

@user-cf3tg8fm8j 10 ай бұрын

@@fearr3951 pretty sure he has a job by now

@Astrea239 8 ай бұрын

How’s life

@flotax3380 6 ай бұрын

Bros in grade 8 learning quadratics 💀

@bashkillszombies 6 жыл бұрын

Of all the math I've learned I've used none of it in the real world. :(

@Kometheus 5 жыл бұрын

I'm sure you've added at some point in your life 😂

@user-nt7ew9di7v 5 жыл бұрын

@@Kometheus not algebra

@Kometheus 5 жыл бұрын

@@user-nt7ew9di7v He said all math 😂

@Boofus90 5 жыл бұрын

bashpr0mpt You don’t use a majority of what you “learn” in school. Simply memorize it and regurgitate it on paper.

@ardanev5564 5 жыл бұрын

90% of algebra will use in the future are Algebra Teachers

@shreyan2426 Жыл бұрын

This formula was discovered by an Indian mathematician Sreedharacharya. I'm so proud to be born in the same country as this mathematical genius.

@JesusIsCometh 5 жыл бұрын

5:17 you can hear gears grinding together in his brain . . .

@inn0version727 8 жыл бұрын

I'm Rick Harrison, and this is my pawn shop. I work here with my old man and my son, Big Hoss. Everything in here has a story and a price. One thing I've learned after 23 years, you never know what is going to come through that door

@Emily-om6mg 6 жыл бұрын

inn0version _ what

@chrisspencer6502 4 жыл бұрын

I've seen this else where, do your home work and clean your room

@Shopbsmaquinasbh 4 жыл бұрын

Lmfao all those NPCS above my comment

@LeeBreezy 4 жыл бұрын

Today i brought in a 1985 handgun that mozart used to kill lincoln

@c3p0worksatburgerking35 4 жыл бұрын

Cheers bro I’ll, drink to that

@heidiborjgmanschmange8485 8 жыл бұрын

I think I hurt my brain. That's quite a formula

@yuanmingrao9266 7 жыл бұрын

Heidi Borjgman Schmange not really I'm in 7 the grade and we're learning it

@hamzaumair7909 7 жыл бұрын

wtf i am in year 10

@MLGRDR 7 жыл бұрын

Trash CAnd Kids are learning harder stuff earlier and earlier. In a few years, we'll have first graders learning calculus.

@yuanmingrao9266 7 жыл бұрын

Hamza Umair yeah i have honors math though, because normal ed. kids are taught this in like 9/10th grade

@m.al3ayel175 7 жыл бұрын

MLG R8DR805 i am studying thing that my brother in collage is studying

@liamgallagher3920 4 жыл бұрын

OK this is mad. I was searching how to do this for my homework and the example he used was the same as my homework question!!

@logankaiser1343 5 жыл бұрын

I'm in a duke program for advanced 7th graders and we are doing an SAT. Before this I didn't understand this. Now I have NATIONAL HONORS for my score of 740

@anonymousanonymous5769 5 жыл бұрын

740 is pretty average...

@nathanaellandicho 7 жыл бұрын

Do you use a computer mouse in doing this? Wow, that control is amazing 😵

@cowsareawesomex 7 жыл бұрын

nathanaellandicho he uses a drawing pad most likely

@jamescobalt1126 7 жыл бұрын

Probably uses a Cintiq or similar.

@jerfersonmatos28 6 жыл бұрын

He always says 'sorry about my handwriting' so he uses certain kind of a drawing pad

@aryanowais3203 4 жыл бұрын

www.onlineuniversities.com/blog/2012/04/de-mystifying-khan-academy-screen-capture-for-educators/ he uses a wacom tablet

@connie6304 4 жыл бұрын

Haani Nehvi i use a digital drawing pad and the curser never leaves even when you move away the pen

@jaahhhdelll 7 жыл бұрын

You are the best. I learn better from you than my teacher in school.. Your techniques are great!

@ChuuChuuPanda 8 жыл бұрын

Monetize all your videos. You deserve the revenue.

@PrebenOlsen90 6 жыл бұрын

Khan Academy is a non-profit organization, however they have multiple donations over 10million dollars EACH, and dozens of donations in the range of 5 to

@jaylottifromthebronx 6 жыл бұрын

Thank you so much i have Algebra 1 regents tomorow and when i was studying i was practicing everything but quadratics because once i looked at the formula i just gave up and never understood it but today you taught me that it is not as complicated as how it looks and now i masterd it and memorized the formula in my head. And prepared for regent exam tomorow all thanks to you!

@greenec336 13 жыл бұрын

Quadratic formula was so confusing for me before! My teacher has to do the most complicated ones first, and you get it in one video! Thanks!

@spacingout. 4 жыл бұрын

this channel is such a lifesaver during distance learning right now. thank you so much!

@SandhillCrane42 5 жыл бұрын

I find this very helpful as learning the multiply to one add to the other factoring, and factoring in general, seems to be a particular case OF this. The general case is what I have needed to understand.

@myownmusic8182 7 жыл бұрын

This is awesome. Right now I'm trying to catch up in my Algebra class because I wasn't paying attention. This has made it, no doubt, a lot easier to do. Thank you.

@vivil321 10 ай бұрын

did you catch up?

@stevenscottoddballz 3 жыл бұрын

Oh, WOW! I have had my Graphing Calculator for DECADES! This is the first time I have been shown how to Graph the Quadratic Formula!! THANK YOU!!!

@renan6827 5 жыл бұрын

Your videos have blessed me so much. Keep up the good work.

@PropKnucklesFPV 5 жыл бұрын

Correct me if I'm wrong, but I find it so much easier to put it into standard form (a(x-h)^2+k) To get to standard form from the general form (ax^2+bx+c), use these: h=-b/(2a) and k=f(h)

@2299star Жыл бұрын

so helpful thank you for also giving visuals on the graphing calculator for the visual learners!

@lukeqiao5477 7 жыл бұрын

if "b" is a negative, does the "-b" part of the formula change the "-b" into a positive?

@manojkumarroy5337 7 жыл бұрын

Luke Qiao yes

@Ana-su7pn 6 жыл бұрын

Luke Qiao yeah

@nbnbnb6549 5 жыл бұрын

Very late. -b when b=-x =--x=-1•-x=x

@givememoney5794 6 ай бұрын

if b is a postive then it will go like - (b) = 1 x (b) and if b is negative then it will go like - (-b) = -1 x -b which is a postive. 7 years late but whatever

@yogobobbread839 5 жыл бұрын

Thank you I am 9 years old and you have helped me so much

@davidfont2596 2 жыл бұрын

Thank you so much for your tutorials and your website. Also, I've watched a few other math channels and you have, by far, the best handwriting. Also, you are concientious of what the view can and cannot see (i.e.: You changing colors @2:19 ). Thank you!!!

@flesh4513 2 жыл бұрын

i swear he uses magic to teach people through a video

@leiaw9287 Жыл бұрын

1 minute into the video and I already saw what I was doing wrong on all of my quadratic formula problems. tysm :D

@pratham2804 3 жыл бұрын

oh my god, thank you. I went to tutoring and they were at quadratic sketching already. You just saved my life as I had no clue what they f they were doing.

@woodsmith_1 7 жыл бұрын

Excellent video. Just discovered the importance of the quadratic formula when trying to solve for x in a more "obvious" algebraic fashion - manipulating values on each side of equation until the variable is isolated... "Double-you tee eff broughe, why isn't this working out" - I thought. Then realized the entire expression ax^2 + bx^1 + cx^0 represents the product of two factored terms, (x + d)(x + e). This can be quite difficult to work out when a and/or b coefficients are values such as 63sin(pi/3), etc. In these cases, where determining factors in a more basic manner is difficult, the great power of the quadratic formula is realized.

@younghentaigod 6 жыл бұрын

when my teacher was explaining it he didn't make any sense but when I watched this video everything makes sense I wish you were my math teacher

@siter931 7 жыл бұрын

Thanks so much I kept getting my anwsers wrong because I didn't realize you had to divide both parts by the denominator.

@akramelsayed5112 3 жыл бұрын

Hows your life now?

@siter931 3 жыл бұрын

@@akramelsayed5112 It's good about to graduate college lol.

@xmariax7711 3 жыл бұрын

This video is so nice because I am just learning that. I am a junior high school student in Taiwan, which is a place next to China, and I thought it was hard before, but after this video I not, this also help me with my math English, thanks for the video and the Up. Now I am going to do my math exam paper. Bye~

@ilanmoore6957 6 жыл бұрын

let's get some *_F R E S H_* real estate. I like how you said that

@devithoka8234 8 жыл бұрын

Thank You!

@ryanho5378 6 жыл бұрын

Thank you 🙏 I just started school today and wanted to be ahead in my algebra class because I’m in 8 th grade and I understood what you did

@dwink7 6 жыл бұрын

Thank you my memories of this is coming back now 😭😂

@chaddinklerwingle2077 11 жыл бұрын

Awesome, very helpful. Thanks.

@nocturnallycan6385 4 жыл бұрын

Very interesting. Thanks for the recommendation Mr.Yenji

@fireghost8045 2 жыл бұрын

He’s doing gods work by teaching me this🙏

@primrosendarevani6412 6 жыл бұрын

Amazing... you are teaching for me... My student finally got this

@thudaolungthi4738 5 жыл бұрын

He says really clear I study at school a whole year but I don't know how to do it because my teacher talks too quickly but when I watch this video I can understand how to do about it thank you!!!

@thedewboyzz 5 жыл бұрын

Got this formula tattooed on my wrist today frig you forever math profs.

@estheriooo 2 жыл бұрын

Funny how we still have to learn this 10 years later

@gia-mariacalbaza4650 6 жыл бұрын

thanks for helping me prep for the act.

@chaseburke9142 4 жыл бұрын

Trust me guys in 20 years we are definetly gonna need this

@sophiakim6145 3 жыл бұрын

thank you for explaining so thoroughly

@chickenfingers4281 6 жыл бұрын

OMG I UNDERSTAND QUADRATIC FORMULA NOW!!! THANK YOU SO MUCH!!!

@OkGringoVlog 4 жыл бұрын

Whoever said you wouldn't need this when you're older lied because today my younger sister asked for some help with Math and here I am having to re-learn what I thought I'd never need to use in the future...

@brondonramdat5399 7 жыл бұрын

You are way better than my algebra teacher thank u

@iknowimstupidbut8084 5 жыл бұрын

This video helped me out a lot. I missed about a week of school and I came back knowing nothing until I saw this video Btw I’m in Math Honors 8th Grade

@mattharris2691 7 жыл бұрын

My math teacher didn't teach this but we just started doing these problems so here I am.

@tristiandang6236 3 жыл бұрын

You’ve help me so much I’ll definitely donate

@kazooeybloo8794 2 жыл бұрын

So inspiring!! I will tell my friend Gene! And share to Churt!

@safiullahbutt5041 4 жыл бұрын

Well thank you for helping us. You are better than my teacher. I will thank you in my Graduation.

@theevangelistchioma 6 жыл бұрын

You really teach better than my math teachers.thanks khan academy

@R0kudo 3 жыл бұрын

Thanks a lot for these videos!

@annfoster1533 8 жыл бұрын

Thank you for the great video. I had a homework on this and needed urgent help. The tutor I found on Vis-a-Vis (mobile app), saved me. Best $20 spent. :)

@joebildan4103 3 жыл бұрын

thanks for the lesson, i truly appreciate how good u are at explaining these kind of stuffs such as math(lol)

@meghajrampure0291 2 жыл бұрын

This makes it so easy to learn quadratic formulas

@Ncs14770 5 жыл бұрын

thanks for teaching this, very helpful.

@acenebula3045 6 жыл бұрын

When I first heard about this, I thought it was going to be bloody hard, but as I started to advance study, I realized it is actually easy, though, it would if my teacher will allow us calculators for square roots😂 Thanks, Khan Academy.

@mottoe2428 3 жыл бұрын

Thank you sooo much honestly didn’t understand it until I watched your videos

@wanfeezah2410 5 жыл бұрын

Wow that is amazing my mark from 30-60 after study with you sir thanks

@noahwaller1812 2 жыл бұрын

that helped so much thank you lots!!!!

@sanskritiseth9698 2 жыл бұрын

Happy to learn with you From India🇮🇳

@stranger-hg1cg Ай бұрын

Was so confuse and five minutes in I already understand everything love you khan academy 💕

@srijitgiri1082 2 жыл бұрын

Hey at least I am now learning something I will apply to two dimensional motion calculations and hopefully my future work

@rithviksrinivas2602 6 жыл бұрын

This man is an absolute legend

@kmoney4648 3 жыл бұрын

I can never learn from khan academy yet I still watch it

@lindahe2433 Жыл бұрын

thank you sir! You help me a lot😁

@cbrock1294 3 жыл бұрын

This explained more in 5 mins then my math teacher did in 4 weeks

@acaciaarmstrong2945 8 жыл бұрын

THANK YOU, THANK YOU, THANK YOU!

@AwaisKhan-vp5ie 2 жыл бұрын

Ur way of speaking is just awesome

@justinaguilar8212 5 жыл бұрын

Thanks Kahn Academy this helped me a lot in math 👍🏻👍🏻

@LePowerPig 5 жыл бұрын

its khan im sorry i feel bad now it gave me OCD

@augustlumanlan2777 5 жыл бұрын

This may be one of the hardest I've ever learned in algebra

@isaacong 2 жыл бұрын

It gets harder

@ashleyaitken8244 4 жыл бұрын

10:38 That is the coolest calculator I've ever seen. I wonder how I could get one.

@rachelt.7123 3 жыл бұрын

Ever get behind class by a week and then watch one video and suddenly you're ahead by two weeks? Haha same

@bigtownbiwwy509 8 жыл бұрын

Thank you so much

@walkingmess5636 4 жыл бұрын

Khan academy explained to me in 15 minutes what my maths teacher couldn’t for a month

@DatBronyBassist 11 жыл бұрын

I was trippin balls watching this and I straight up memorized it. Better than my actual Algebra class was.

@danae6393 4 жыл бұрын

Em I the only one that is still Confused 😭

@redicd6857 4 жыл бұрын

nope me

@mckenzieedwards527 4 жыл бұрын

me too 😂. i still don’t get the plus or minus part

@louisesanchez. 3 жыл бұрын

im literally so confused too oomg, and my end of semester exams are tomorrow :(

@poojakissoon8374 3 жыл бұрын

same here

@andrewwilkerson8186 3 жыл бұрын

@@poojakissoon8374 so with the - or + part there are two possible answers.

@FireMageGaming 10 жыл бұрын

what did he do to the 2 in the last example? when he divided by the negative sic from the negative twelve he just forgot about the two. wha happein?

@scorpion3705 9 жыл бұрын

+Mentic He divided all the terms by 2 to simplify, that's why the -12 became a -6, and the -6 became a -3, and the 2 square roots of 39 become one square root of 39, which is why there is no 2

@emmanuelamoh7181 7 жыл бұрын

Thanks, I understand now.

@bavabangarsd7267 5 жыл бұрын

This kiddo

@JoeMama-tf3pn 3 жыл бұрын

@@scorpion3705 only one year late lol