Finding the vertex of a parabola example | Quadratic equations | Algebra I | Khan Academy

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Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.
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[@RobertMurphy-wm3ge]

Thanks for these videos, Mr. Khan I consider you the Bob Ross of Mathematics.

[@yourmomdotcom4861]

Hhahaha good one!

[@haxjason4826]

khan academy explains things like 5 minutes my teacher couldn't explain in 1 year xd

[@shrawanipal]

istg

[@yourfavouritebestied3669]

fr

[@_bloxxer]

Just pay attention then 😂😂😂

[@cowsareawesomex]

thanks for this man you are quick and to the point unless other chanels. keep making these videos or else i will fail my class.

[@haoyangli5781]

All of us are here because our teacher hasn't done their job very well, indeed, we all have useless math teachers.

[@dylancordeiro5819]

@@haoyangli5781 true that Haoyang

[@mahmoud-quran]

Haoyang Li nah, my teacher is great. I just need extra help

[@srejonnath4085]

Same

[@sirinxoxo8031]

Yeah like my teacher teaches very well but i just don‘t listen or understand because i‘m stupid

[@deyarfaraj2512]

This man is the reason why million of people pass their finals yearly We need to find a way to pay him back Thanks Khan we all appreciate it ❤❤❤❤❤❤❤❤❤❤

[@Happy-Me.]

I would rather remember the formula for the Vertex!

[@katiw397]

Mr GShocker then again, if you get the standard form and need to find the vertex, then-- 😂

[@eladpeleg745]

I actually really liked the second technique. It's quite elegant.

[@edwardsstephen252]

I was out for a day and i missed this lesson. i almost failed a test because of it. Thank you for this video. it has help tremendously! I am sending this to all my friends who are having trouble. Thank you once again!

[@Gusthesaltybus]

How'd that go?

[@feymob5711]

I LOVE YOU BRO!! My math teacher got suspended and our substitute is really bad at teaching (no offence), I'm in grade 10 and people keep warning me that the transition from grade 10 math to grade 11 functions is stressful (I already signed up for AP). Anyway my teacher never taught us the simple formula of finding the vertex -b/2a he taught us to calculate the axis of symmetry by dividing the 2 factors by 2, anyways it was a mess and i didn't understand, but this fixed the last piece in my puzzle, people reading this might not care much but I just really want to thank you for what you did, you saved a life♥♥♥♥

[@caadenator86]

You are the reason I'm going to pass algebra 1.

[@mxnstr1346]

im in 7th grade and im doing it rn

[@caadenator86]

@@mxnstr1346 I took algebra 1 in 7th grade too lol

[@duckduck6569]

@@caadenator86 hi

[@duckduck6569]

@@caadenator86 what are you taking now

[@angelika77st]

I get confused with the finding of perfect squares. =/

[@innkblot5224]

I understood the first part, the second.... not so much...

[@christianjt7018]

Great explanation. I have learned a lot with Khan Academy. Thank you very much.

[@abdullahhamadeh]

iam confused.... from were the number 4 came ? in the part were y=5(xsqure-4x+"4")+15-20. please some one answer me

[@abdullahhamadeh]

you don't know me yet ;) ... i can be lazy but that photo is when i didn't go to the gym ......😒

[@sydneycampbell1097]

abdullah hamadeh it's cuz he found half of the coefficient of x and then squared it So half of four is two and two squared is four😊

[@abdullahhamadeh]

thanks alot :)

[@bhairavipras6744]

@@xMaTTyZ what the hell. Why?

[@dylancordeiro5819]

@@xMaTTyZ ur not funny

[@couchpotato6274]

thank you so much I was so confused and I have a test coming up. Helped me a lot

[@mohammednourinjerini6527]

Your explanation is excellent so much. Thank you.

[@AG-ec3bz]

Im literally a whole 14 years of age and somehow finding the 2nd method challenging. :(

[@Thready704]

im 20 years of age and finding everything challenging

[@jacksonneppl4868]

Who needs parabolas? Like actually :(

[@Thready704]

@@jacksonneppl4868 right, this makes me wanna kms but this precalc class is required for my transfer . I'm not even gonna use it in my field of work

[@Thready704]

Sometimes I think college isn't for me

[@jacksonneppl4868]

Matt Franklin This is my freshman high school math homework:(

[@narekkazarian4943]

Great recap on finding the vertex. Thanks Sal

[@squirrelguy5673]

Great video! I was struggling with graphing parabolas on AoPS before I saw this. Thanks!

[@itzcheckers6697]

aops 😭😭😭

[@asadmuneer8654]

I'm really thankful to you, Khan Academy!

[@extracrispytea]

This makes so much sense thank you

[@karinatejeda8266]

The point of this video is to allow people to be able to see the lesson step by step!

[@aaaa1111muffin]

A way faster way of doing this is by differentiating the function and setting the output equal to 0 to find the critical numbers, which would only return one if you're talking about a parabola since its only to the second power. d/dx (5x^2-20x+15) 10x-20, set it = 0 10x = 20, 20/10 = 2 You don't have to remember a formula to do this either, you could do it in your head

[@latterdaypal765]

Ah yes. Thank you. In my algebra 1 class I now know calculus. Thank you.

[@stephenwithaph1566]

Sick.

[@rttt8532]

Thank you so much for all your help!

[@beckybinning2278]

I watched this video before my mock exam and thought I had it totally right and then this question came up: a parabola has an equation of y=X squared / 10 -3x how do I find the turning point?

[@aaroldaaroldson708]

My favourite math channel btw :)

[@yungsoy7561]

Who else learn more in this one video than in a week of school

[@junodisarapong6635]

You and a friend are out hiking across a large flat plain anddecide to determine the height of a distant mountain peak, and alsothe horizontal distance from you to the peak. In order to do this,you stand in one spot and determine that the sightline to the topof the peak is inclined at 7.5° above the horizontal. You alsomake note of the heading to the peak at that point: 13° east ofnorth. You stand at the original position, and your friend hikesdue west for 1.5 km. He then sights the peak and determines thatits sightline has a heading of 15° east of north. How far isthe mountain from your position, and how high is its summit aboveyour position?

[@psun9039]

thx for helpin me pass my math class dawg

[@josenelson3707]

Thanks for the video, its really helpful😊

[@jam9676]

"Con" might be a homonym for the first name of this Academy, but this is some of the most honest math I've ever seen.

[@aaroldaaroldson708]

the second apporach is the easiest one. Also really intuitive

[@musawirahmad7046]

wonderful explaination, thanks alot

[@assaaddawood4440]

1:22????

[@yashuppot3214]

could also solve by setting deriviative equal to 0 and solving for x

[@omathias0240]

This video is very helpful even if you don’t have a coefficient. Would suggest to anyone.🔥

[@Alkimachos]

I've used this channel from my first years of elementary school, to my first year in collage, and I will continue to use this channel. Keep up the hard work king

[@denisemanalang3525]

Would these also apply if the linear term isn't present?(like in ax^2 + bx + c, there's no bx). I find trouble in getting the vertex without graphing it

[@DANIELDALLAS_MATHs]

Yes, the x-coordinate of vertex is just 0

[@skusaid8512]

OMG! Sir splendid!

[@albertvalencia5786]

Is there any advantage to using completing the square over the formula? In later Math classes or anything?

[@mxnstr1346]

lmao

[@thejiminator8816]

what about P=RI^2, where their is no bx term, would P just keep getting smaller with increasing values of R due to V=IR, y=ax^2+0+0 has the line of symmetry of 0, but this cant be the case for P=RI^2

[@jaskull5056]

Breh this dude has literally made me get such sick grades! if yall do not understand him idk what ya doin

[@khalilac17]

Can you elaborate more on your videos? What happens if you can't complete a square?

[@johnmurphy9023]

You should have told about the Yv, which is equals to -"delta"/4a... Where "delta" = b^2 - 4ac.

[@remasalshehri7925]

you saved my life thanks

[@aidanreed6268]

These videos are lifesavers

[@HelloHello-vq5fw]

Thx dude helped a lot

[@jonathancipriano9312]

1:06 waohh what?!?!?!?!?!?!?!? I never saw that formula before!!!!! IM USING THAT ON MY TEST TMR!! GENIUS!!!!

[@xaviersfinance2664]

How did u do on the test ;)

[@vedant2346]

yea how did u do on the test Jonathan ;)

[@Mr59J]

I like the second method but when youre working with irrational coefficients its unnecessarily hard to use

[@abdulbasit5276]

Thanks for this lesson

[@linyokwen3987]

Thank you very very much!😭

[@theophrastusbombastus827]

He is efficient, explains thoroughly, and doesn’t complicate things. You have my respect sir.

[@matthewwheeler2443]

watching a bunch of these before my final😍

[@ianvillaluz8279]

Holy crap thank you, personally for me I find using the formula easier

[@thejiminator8816]

In the former I would like to know at what point P is lowest with R

[@mindreader131]

Just a thought. Take the X-intercepts and average them. That is the line of symmetry, giving you your X value for the vertex. Then, plug the x value in to equation.

[@AoSCow]

That only works if there is an x intercept

[@Ngalicious1326]

Hopefully this helps me in my retake test tmrw before summber break or else im cooked

[@ajwooten4343]

Bro just hit the big brain maneuver

[@sirinxoxo8031]

Why‘s that (x+a)^2 ?? On the top right corner. Please i need help

[@jacesimon5013]

Hey, I was just wondering what site you use to make your videos on maths, physics, bio, etc...

[@syddhant19]

Khan academy

[@agerestricted9574]

😂

[@agerestricted9574]

He means the program

[@basedguns8218]

@@agerestricted9574 😂

[@marthacrawford5085]

Were did you get the -5 again

[@subsoar5734]

Thank you Sal, you freaking king

[@acetabuada7526]

Where did that 2 came from? referring to the 2 that was multiplied on 5 and 20. Is the number 2 constant or not? Or maybe it came from the answer of -b/2a? I'm sorry, I'm not a fast learner. Hahahaha. :) Please answer me. Thank you in advance.

[@WeakestYogurtEnjoyer]

Wish he used parentheses

[@elizabethserra3797]

THANK YOU! :)

[@murtazahaque2815]

Math is really fun, and Khan Acadeny really helps with learning the things I love. Thank you so much for making these highly helpful videos!!

[@David-hh8on]

5:08 so the x vertex can not equal to a negative right? but why ?

[@icefox6535]

When you were literally crying during homework and this vid saved ur life😂

[@pranavgandhi9224]

Amazing ty

[@alpanaagarwal9261]

From where did -b/2a formula came please someone explain at 1:22 pls pls pls !!!

[@agerestricted9574]

How quick you need help? I’m a day late

[@sohaibahmed226]

you can just type that in the calculator and find it or if solving manually just factor it

[@chesterduanesese7339]

Thank you so much😊

[@TabmansTube]

where is the video of how this x vertex formula is derived?

[@bigdog3628]

OK so lets say that -20 was positive, then the x portion would be -2 instead? Or can it only ever be a positive value?

[@BobBob-uv9fq]

Can yea do a video when yea have turning points but not having midpoint

[@nachhilfeerfolg969]

@5:09 why is that term always positive or zero? What's the proof of that?

[@LenniAalto]

I love you very smart stuff

[@gertwiebach2169]

Why did you not divide ALL terms by 5 at the beginning, but only 5x^2 and 20x? But if you divide all terms by 5, I mean the 15 also, you get completely different minimum value, why is it so? EXPLAIN IT PLEAASE

[@isaiahwhite4933]

THANK YOU!!!!!!!

[@user-nj8to5ug6d]

4:47 what about the +4 ?

[@guillermoguzman6301]

Why can't the X in the final equation go below zero? What rule is that and why does it exist?

[@chloe10257]

thank you, this helped me more than my actual teacher💀

[@BobBob-uv9fq]

Yea can complete the square as well?

[@ellena.n385]

what if the equation is in the form y=a(x-h)^2+k?

[@DANIELDALLAS_MATHs]

It is already in Vertex form V(h,k)

[@biggypupps9628]

were dose the 4 come from

[@biddybonga]

Helping me through 8th grade

[@xaviersfinance2664]

Same ;)

[@sinner.stranger969]

Just do d=b2-4ag to find x1 and x2

[@williammccoy6155]

literally the only reason im passing

[@thejiminator8816]

With a constant 5 volts

[@dionnetugade3960]

Thank you

[@Udyat2009]

Thanks

[@wafflingbrit1178]

Cheers mate

[@okmotivated4786]

Is there anyone else , who is tought parabola on school in Grade 9?? 😢😢😢😢

[@kotoamatsukami3362]

[@persismichelle3063]

this is so helpfulllllll

[@step938]

good video

[@muiiriss_]

what abt finding the vertex in an equation like f(x)= 3(x+1)^2

[@basedguns8218]

The coefficient in the bracket is K or where the vertex will be on the x line. The 3 is A. If it's positive it will face up. If negative down same for K. Hope I helped your test 8 months ago

[@muiiriss_]

@@basedguns8218 omg i completely forgot abt this video. Thanks lmfao

[@basedguns8218]

@@muiiriss_ no problem hope I wasnt to late lol

[@muiiriss_]

@@basedguns8218 no lmfao you’re actually just on time

[@basedguns8218]

@@muiiriss_ thank you good luck on the thing youe doing

[@dayarojas8699]

what about x^2+2x-3

[@leagirl6601]

thank you

[@cupcakesquash]

YOUR VIDEOS SAVE MY LIFE IN MATHS AND CHEM

[@hari4345]

thanks to you i dont have to by heart anything😄

[@nifte4635]

Ur my new best friend