Parabola vertex and axis of symmetry | Quadratic equations | Algebra I | Khan Academy

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Parabola vertex and axis of symmetry
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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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[@DynastyJr]

ill take the shortcut

[@bethmoth22]

I was lost then you explained the quicker way. Thanks

[@munchlol4327]

you is old

[@StrawhatPizzle]

My man Sal always coming in clutch

[@slippery5932]

I got lost

[@lalamia1981]

Me too

[@yajrainc1594]

@@lalamia1981 me 3

[@kd0197]

Me 4

[@koib]

Me 5

[@connzerjess1665]

Sorry to hear about that, here is direction back to where you started so you can try again until you succeed: 0:00

[@jenxberry8332]

I just learned more in a 7 minute video than in a whole week in my Math class. *gReAt*

[@WesternkindUnited]

slow and intuitive way no exact opposite of what I need. I need a simple formula to apply and get this miserable experience over with.

[@sazzyjaxaphone7581]

These videos are lifesavers

[@Bella-do5sh]

This is why I love Khan Academy. You always answer the question why?

[@zaraf8353]

I now may not fail my maths test tomorrow so thanks

[@helenpetersen447]

Oh.My.God. BRUH that shortcut may have just saved my final tomorrow! Why didn't my teacher have the foresight to teach us that!!! I've been confused on the vertex for two weeks! 😧😧😧

[@bisratkubi871]

Well....

[@UGLYRAED]

YAY now I know both methods. Quick and dirty is not allowed on youtube.hope this video doesn't get deleted

[@julie8990]

.....9 years ago ....,

[@Roxanne3v]

Come on down to Olive Garden and get yo free breadsticks 🥖🥖

[@popeyes3830]

The quarantine packets don't teach squat so ty so much Also if your hear for Axis of Symmetry or shortcut then it starts at 6:28

[@soulchronicity]

im sorry if this seems rude, but do you mean "if you're here for"?

[@callisto742]

Thank you!! I am a big fan of the slow and intuitive method. The quick formulas makes no sense for me. Although in an exam it might come in handy.

[@michalvojacek1292]

Or, using calculus, which might be harder to do, but is more intuitive; you could set the equation's derivative equal to zero and solve for x. Because a derivative of a function is the rate of change of that function at a specific point, the vertex would be where the rate of change is zero, or, to put it geometrically, where its tangent is parallel to the x-axis: (Using Lagrange's notation) Useful: (x^n)' = nx^(n-1) (-2x+8x+8)' = 0 -2*2*x+8 = 0 -4x+8 = 0 -4x = -8 4x = 8 x = 2 To get the Y of the vertex you just have to evaluate the original expression at the x we got: -2x^2+8x+8 = -2*2^2 + 8*2 + 8 = -2*4 +16 +8 = -8 + 16 +8 = 16 + 8 -8 = 16 And there you go: The vertex is at [2; 16] (Btw. if you don't know what I just did don't worry, you'll learn some day)

[@michalvojacek1292]

Calculus is intuitive once you understand it (epsilon-delta and the appropriate limit formula for instance). But to understand it, one has to stop being useless in the comments section and actually have a go at calculus. (Not to mention having some basic forum behaviour, like not swearing and not replying to 10 months old comments)

[@ImNaviar]

Well, sir, I was making a joke--rather than actually being upset at what you had to say, but since you're one of these people who thrives on obtaining what you see as superiority over others through self-proclaimed intelligence, let's go ahead and involve ourselves in a bit of an argument. The definition of intuitive is as follows: "using or based on what one feels to be true even without conscious reasoning; instinctive." Mathematics is, in absolutely no possible aspect, instinctive. Math is a language that one must learn in order to understand it. Now, if you're saying "intuitive" in an attempt to articulate the intuition one may have if they already possess previous understanding of math, then you're using what is called a stipulative definition, which is illogical when supporting a claim. Essentially, what I'm saying is, you're showing us that you are not as smart as you are trying to appear to be. You may know math, but I know arguments. As a matter of fact, my job is to train students on structuring argumentation, so this is water I doubt you want to swim in.

[@michalvojacek1292]

en.wikipedia.org/wiki/Srinivasa_Ramanujan

[@THE16THPHANTOM]

I'll take the hooligan formula thank you.

[@jffrysith4365]

Thank you. Ive been trying to teach this formula but I didnt really know how to derive it because its not taught in NZ. I figured it out half wah through the video because your explanations are amazing!!

[@Echo-wp5ul]

Good video, with a small error at the end : for x=3 y=6, not 8. for y=8 value of x must be 4 - which is visible on the graph

[@stephhmph95]

THANK YOU FOR TEACHING ME. Unlikes my teacher has been able to.

[@xue6065]

Lol when ur math teacher just goes “watch khan” 😂

lol

[@demshi1]

thanks bro!!! i finally got it! after hours trying to figure it out how to graph q. f . ^____^ u made it easy for me . u r the best !1

[@naomidemenezes9626]

Algebraically arranging the equation definitely helps out when looking for or defining your maximum or minimum point. Although, the quick and dirty way of finding the vertex is simple and a lot quicker than going through each step to find the vertex.

[@luisdfernandez2601]

Awesome instructions. I thought it was crazy to just out of nowhere add a +4 and -4 on one side of an equation just to make things work out. I didn't know you could do that. Very good to know. Thank you!

[@lucysong885]

I was confused at first....

[@jessyleong5005]

Why does the shortcut formula work? Is there a video on it?

[@ashleyyyu1680]

i remember watching this before and was confused asf but i literally get it now--

[@DanNguyen-th5gp]

screw slow and intuitive ways

[@bbrown9763]

It seems like "screw slow and intuitive ways" is the right answer, but, if you don't understand what you're doing and why you're doing it, it's a lot easier to become lost when you get into more complex math. "Following a process" is part of the problem with how math is taught. You're just going through the motions, instead of knowing what to do because you understand the material.

[@omarkamel9608]

very, very useful

[@LucyRockprincess]

i bet you get this alot, but THANK YOU

[@GndmMkv]

quick n dirty... lol

[@TheJakehunter]

Fuck this shit is so complicated. :/

[@jawadbadkook9771]

I'm speaking about the quick way. how can we find y which is = to 16.

[@richardding4821]

thx alot

[@sri-kaushalramana437]

wait how do u get the y value from the shortcut, didn't say

[@falcondarkshadow]

You substitute the value back into the original equation. Then solve for Y. Example: X = -(2) / 2(1)=-2 Y = x^2 + 2x + 4 -> Y = (-2)^2 + 2(-2) +4 -> Y = 4 - 4 + 4 -> Y = 0 + 4 -> Y = 4

[@whatisthat7874]

Where is the 4x go between step 2 and 3 of the first way...I’m lost

[@zeraliii6150]

Sir when u visualized saying if x was 0, then you said it would be equal to 8, which i understant. How did you get 3??? You simply said if x=3 then it would be equal to 8 too.

[@benhuston310]

Makes me want to cheat. but I don't cheat.

[@belisauros370]

If I could like this video more than once I would

[@JamieChen786]

...This? Wait till geometry. :P

[@miralee3635]

Guys if you can find a common multiple of ‘a’ then u can just divide it out without using perfect squares

[@asadzaman7616]

in 6:08 something interesting when x is equal to 4,y is going to be equal to 8

[@SmilerBFC]

need isopleths and constraints examples

[@LemonJuiceGV]

used formula to find x bit can't see how to get y without using the long method

[@moonlightfragments7900]

You substitute the x value you get into the equation and get y from that I think ?

[@e.hamrick9932]

3:40 That is not always true. If you substitute 2 for "x", and then complete the operation inside of the parenthesis and then square it, then you won't have a positive number. You will get 0, which is neither positive nor negative. 3:52 Same thing, it won't always be negative. If you have a difference of 0 in the parenthesis like I explained earlier, then you will not have a negative number (since zero times anything is zero), but rather, zero, which is neither negative nor positive. Thank you for taking the time to read this.

[@bisratkubi871]

I got lost so I watched another video and came back...and it was better

[@juliesandler4664]

I appreciate u trying to teach us but u talked WAYYYY to fast and I couldn’t understand quite nicely

[@Suresh-rl5zr]

What was the equation at the start.

[@raulc02]

So why can you only use (x^2-4x+4) and not the whole equation... Also when you distribute the -2 ... Why is it still parr of the equation... This confused me -.-

[@Akiithebest]

I reckon his favourite word is 'intuitive' :P

[@PickleBeanBoss]

freaking legend

[@jackng3873]

tbh i dont understand crap, still better than my teacher, thanks

[@ashgrey8304]

I don't understand. When he multiplied what is inside the (), shouldn't the -2 outside be used to multiply it and thus wouldn't be there in the next line? I'm sorry if I am not making sense, but you know, like many others around here...my homework is also due tomorrow lololol

[@ashgrey8304]

Actually nvm, lack of sleep has addled my brain. It makes sense now

[@053_abdulhannanbhat8]

thanks

[@IanSerranoBengoa]

i came here for the axis of symmetry... where did you explain that? bro the mumble you made was so fast i almost didn't catch, and well... i didn't understand it either but i got everything else, you are a pretty good tutor, just dont put axis of symmetry in the title if you aint going to explain it, or even write it. still 10/10, love the colors!

[@easyescape5211]

Stfu u dirty doorknob.

[@moonlightfragments7900]

you can get the axis of symmetry from the vertex as the y coordinate of the vertex will give you the axis of symmetry

[@rayj.9568]

He stated the axis of symmetry at 5:38 - 5:45.

[@zyleafpunch5684]

Weird method but it's fine

[@edshondasi737]

What if u can't factor?

[@sunwooloml4301]

what object is this?

[@Putt-Putt]

2:12 How does -2^2 give a positive 4? Shouldn't it be a -4 instead?

[@cocoa_cakes4938]

It’s -2 times -2 which is positive 4

[@DanielGonzalez-wx9cg]

What if there is no x? Only one x and not the second x

[@theevangelistchioma]

Wait how did he get 3

[@walter8206]

I have an assignment that is due in 5 hours and I haven’t done ANY of it!!!!!!!! HELPPP

[@rinokumura6580]

I still lose but better then my teacher

[@cytusallcore]

the blue exorsist was an awsome anime. wish i had your name for youtube

[@EmoVince101]

When i came searching for this, i was hoping for something different. But apparently it's the same way my teacher teaches, and i have come to realize that i am just lazy... Got anything to help lazy???

[@cardboardbox331]

Well, it’s been 8 years, so hopefully you’ve worked it out by now

[@meggiemcmurray5177]

I’m completely lost

[@lazyhippo1610]

the mic is bad

[@Kaylo.Art.Designs]

Why can't I understand what is happening here lol

[@_kilyy_]

Dont take IB A&I 😭🙏

[@serxhio5006]

What

[@briancohen4269]

Error at 6:08. It's when x=4, y=8.

[@IanSerranoBengoa]

Brian Cohen no bro, look at the parethesis, he multiplied the eight by 2 and why four???

[@dingdong3021]

@@IanSerranoBengoa to get y=8 x should be 4

[@IanSerranoBengoa]

@@dingdong3021 i don't remember this stuff anymore 😂

[@IanSerranoBengoa]

@@dingdong3021 i got an A so im gucci

[@cytusallcore]

try yaymath or thinkwellvids. they do better explaining then this "dude" (look up the meaning of this word. you'll never call anyone a dude again

[@joshuasanderson3911]

I hate math 😦😧

[@username-jm2bn]

M O O D

[@KoloSokame]

Badly explained...get to the point

[@cheems1358]

maybe it's you that's the problem. this man has his own website with millions of users that get help and i understood it perfectly fine. mans has ted talks and makes millions so he explains really well.