here's my own explanation, if you are confused: ----------------------------- - a quadratic equation makes a parabola (curved line shaped like a "u") - parabolas usually go through the "x" axis two different times, meaning that "y" will be equal to zero at both these points - therefore, to solve quadratic equations, you need to make two equations to represent "y", then set both equal to 0, and finally solve both for "x" - go to any question on your homework, and start by looking at the quadratic equation you are given. chances are, it is in the form "Ax^2 + Bx + C = 0" with A, B, and C being constants. as i said, the first step to solving this equation will be to make it into two equations. so how do we do this? - one common way is to use the quadratic formula, which Sal wrote at 5:41. to use this formula: look at your given equation, find the values for A, B, and C, and simply plug them into the quadratic formula. now you should have a new equation, very similar to the formula except with "x" as the only variable. - now, we will split this new equation into the two smaller equations we need. this is where the "±" symbol comes in. - first, duplicate the new equation. now we have two identical equations, let's call them Equation 1 and Equation 2. - then, change the "±" to a "+" in Equation 1 and to a "-" in Equation 2. - step #1 complete! we have made two equations that represent "y" - step #2 is to set both equations equal to 0. however, the quadratic formula already handles this for us, because our given equation was equal to 0 in the first place. so in this case, step #2 can be skipped altogether! - last step is to solve both equations! for each, evaluate the radical first, and then you will be able to simplify the entire fraction. do this twice, and you will get both solutions for "x" ----------------------------- hopefully this helps. good luck, i believe in you
sal helped me understand concepts in eighth grade when my teacher just assigned problems and explained messily. Sal is now helping me again in tenth grade, when my teacher just says “you guys should know this!” instead of actually telling us what we need to know. I understand this so much better. before, i didn’t know how this related graphically. i also didn’t really understand why we were using that big discriminate function. now i do! thanks sal you’re the best teacher ever
I was a middle school / high school math teacher for 19 years, so I'm well-versed in these mathmatical formulas that are essential for students to understand & use successfully. Yes, it was kind of messy. :) But your demonstration was simple & nicely demonstrated. Great job!! I will be recommending you to several family members & friends who homeschool. Thanks for enriching their learning!!!
After 15 years later of making this video, have I watched.I am benefitted. Thanks doing such a necessary work where many of us doing many unnecessary jobs. I have been clear after doing own class of mine. Thanks again!
A quadratic equation is just a second degree equation that has x squared and x as variables, such as 4x^2 + 5x + 3=0. Using the quadratic formula, you can solve those types of equations.
سبحان الله وبحمده سبحان الله العظيم استغفر الله العظيم الذي لا إله إلا هو الحي القيوم و أتوب إليه سبحان الله وبحمده عدد خلقه ورضا نفسه وزنة عرشه ومداد كلماته اللهم صَلِّ وسَلّمْ عَلَى نَبِيْنَا مُحَمد ﷺ
Its factoring trinomials. The second term(-x) has to found by adding 2 numbers and the third term(-6) has to be found by multiplying the same two numbers. 2+-3=-(1)x and 2x-3=-6, (x+(-3)) and (x+(2)) You can also use the FOIL method on these numbers to go back and solve your original equation. Or you could just use the quadratic equation.
I’m in 7th grade learning this and the math teacher did not explain it well enough for me to understand. This video actually explained it well thank you.
I agree! I thought I had it down, but after watching this I am now even more confused. Step by step instructions, please! Do you know of any other video I can watch that would explain how to do this better?
He is explaining it very well and clearly, like he always does, you should go and read up on algebra I in order to understand the concepts he is introducing.
I am afraid to say that I see a minor mistake in the polynomial x-squared minus x minus 6. The error lies in the graphing. The parabola's vertex is (1/2, -25/4) not on the y-intercept as you pointed out. The y-intercept is merely where the parabola hits not where the parabola starts. You can find the vertex by using the formula -b/2a.
actually if you solved it along w him, its really easy to understand. just require some basic mathematical understandings like factorization etc. mans doing a good job imo
thanks I'm tryin to prove to my stupid school how smart i am I'm goin to to ahead and learn everything ahead of time I'll be in tenth grade next year learning about geometry and I'll be teaching my teacher about calculus! i bet theyll change their minds and let take the accelerated classes then!
a quadratic equation is an equation that inviolves x to the of 2 (x^2) but does not involve x to any greater power (fx: x^3) nor any square roots exponential funktions or any other funky stuff. quadrtic equations go by the form of f(x) = Ax^2 + Bx + C though you could also write y instead of f(x).
14 years later now and i stil struggling with maths but this guy always makes me remember this for a day and then I against start forgetting but remember his wise mathematical words
if you have x-3=0 or x+2=0, you get that because when you are looking to find x, x will ALWAYS be the opposite of what was in the equation. For instance, x+24=0 or x-9=0, x will be equal to -24 and the other x will be equal to +9 because of opposites.
Err if you throw a ball obliquely, it's ideal path can be represented by a quadratic. You can find out how far away it will land (y =0) or when you drop a missile, it traces path which can be represented by a quadratic if you don't count in the effect due to air friction etc. So approximately if you solve for Y = 0, you are finding out where it lands
The quadratic equation is used when you don't know (for example) what two numbers add up to get -9 and multiply to get -10. The guy didn't even need to use the quadratic equation he should have multiplied the one by negative 10 and factorised it that way. I was also pretty confused at the end of the video.
Thank you for making Math fun for me, after 20 years of leaving school I decided to go back to school again. I only wish my teachers at school could have made Math so much fun for me as you do. I wish you all the best and hope you continue doing this.
x²+6x-7=0 x=-6/2±√((6/2)²+7)=√16±-3 x#1=1 x#2=-7 pq x²+6x-7=0 x=(-6±√(6²-4(-7)))/2 = (-6±√(36+28))/2=(-6±√64)2= X#1=1 X#2=-7 I prefer the pq formula instead of the quadratic formula because it has fewer steps to calculate. Here it is written down x=-(p/2)±√((p/2)²-q) the only problem is when you have a value behind x² so you have to divide that away. Both have their problems.
Barrons PSAT/NMSQT 8/9 Study Guide Premium 2023 actually took this first question from Sal. I am currently in the "Passport to advanced math" section, and I got shocked seeing that was Sal's question. Just something I wanted to share with you all. The page number is 419 Question 13.
+Videh Patel the idea of the example is to demonstrate the quadratic formula. since it can be also be factored, you are then able to show that the quadratic formula produces the same (correct) solutions. i'm pretty sure he chose a polynomial as his first example that had rational solutions so that he could connect the idea that the solutions are geometrically equivalent to the x-intercepts.
I need help. Every question I do I always end up with a decimal even when i'm not supposed to get one. I JUST DON'T KNOW WHAT I'M DOING WRONG. It happens every time I do a square root.
![KSI - Dirty [Official Visualiser]](http://i.ytimg.com/vi/VoDh1h1dPUE/mqdefault.jpg)
here's my own explanation, if you are confused:
-----------------------------
- a quadratic equation makes a parabola (curved line shaped like a "u")
- parabolas usually go through the "x" axis two different times, meaning that "y" will be equal to zero at both these points
- therefore, to solve quadratic equations, you need to make two equations to represent "y", then set both equal to 0, and finally solve both for "x"
- go to any question on your homework, and start by looking at the quadratic equation you are given. chances are, it is in the form "Ax^2 + Bx + C = 0" with A, B, and C being constants. as i said, the first step to solving this equation will be to make it into two equations. so how do we do this?
- one common way is to use the quadratic formula, which Sal wrote at 5:41. to use this formula: look at your given equation, find the values for A, B, and C, and simply plug them into the quadratic formula. now you should have a new equation, very similar to the formula except with "x" as the only variable.
- now, we will split this new equation into the two smaller equations we need. this is where the "±" symbol comes in.
- first, duplicate the new equation. now we have two identical equations, let's call them Equation 1 and Equation 2.
- then, change the "±" to a "+" in Equation 1 and to a "-" in Equation 2.
- step #1 complete! we have made two equations that represent "y"
- step #2 is to set both equations equal to 0. however, the quadratic formula already handles this for us, because our given equation was equal to 0 in the first place. so in this case, step #2 can be skipped altogether!
- last step is to solve both equations! for each, evaluate the radical first, and then you will be able to simplify the entire fraction. do this twice, and you will get both solutions for "x"
-----------------------------
hopefully this helps. good luck, i believe in you
Nice!
Thanks
Thanks for making the work
You should help me lmao.
Appreciate it
This is the most complicated simplification I’ve ever even heard of
Literally
yes Same!!
:)
Yes
you have no idea how much this helped me understand
xd
me wondering how a mouse pointer with a voice is the best math teacher I've ever had
Very funny 😄😄😄
No cap
I’m learning a few years above my grade every week lol
13 years later and still being watched around the world
This made me feel stupid
@@mohmedalgahmi8881 k
hmm
@@mohmedalgahmi8881 bro no need for such compliments instead you can get satisfied by your answers
14 years*
sal helped me understand concepts in eighth grade when my teacher just assigned problems and explained messily. Sal is now helping me again in tenth grade, when my teacher just says “you guys should know this!” instead of actually telling us what we need to know. I understand this so much better. before, i didn’t know how this related graphically. i also didn’t really understand why we were using that big discriminate function. now i do! thanks sal you’re the best teacher ever
I'm in 10th grade too and could not agree more.
I'm in my second year of college and it's still helping😅
I am doing this in 7th grade, and it makes sense now
Not sure what to say
17 years later and still a life saver
real
couldn't agree more XD
I was a middle school / high school math teacher for 19 years, so I'm well-versed in these mathmatical formulas that are essential for students to understand & use successfully. Yes, it was kind of messy. :) But your demonstration was simple & nicely demonstrated. Great job!! I will be recommending you to several family members & friends who homeschool. Thanks for enriching their learning!!!
You still here?
@@OkIPullUp2915 r U still here?
@@scoopsthestandard Maybe
Hey wait it's been ten years
This comment is 4 years younger than me
Everyone asking: WATCH THE FACTORING VIDEO BEFORE THIS ONE.
Also, a negative * a negative = a positive. Thus -9^2=81
whats the title or link because there are many factoring quadratic equation videos by khan academy
No (-9)^2 is 81, -9^2 is the 9 squared only
aren't they the the exact same? as they both end up with the same answer: 81.
boi u dumb
-9^2= -(9^2)=-81
but (-9)^2=-9*-9=81
81 does not equal -81
what do you mean?
2 hours of class, I don't get it. 3 minutes of video, I got it!
😂😂
You're great I hope you get to be a professor because you tech better than some.
After 15 years later of making this video, have I watched.I am benefitted. Thanks doing such a necessary work where many of us doing many unnecessary jobs.
I have been clear after doing own class of mine. Thanks again!
I hope your classes are going good! :)
@@nocturnalvisionmusic tysm
@@ジェリエル aww you're very welcome ^w^
A quadratic equation is just a second degree equation that has x squared and x as variables, such as 4x^2 + 5x + 3=0. Using the quadratic formula, you can solve those types of equations.
As an Asian I felt compelled to watch this and as an Asian I want to do more of these equations
nerd
?
@@noahyemane4609 Dude I watch these for pleasure since i'm 13 yrs old and wanna become knowledgeable this doesn't mean i'm a nerd.
@@Watterso shut up nerd
Sal has been using RUclips practically since it was born! Technologically speaking this was way before its time!!
0:43
Good job!!! You're great I understood and followed your example I made good notes from your presentation. Thank you, keep up the great examples.
I’m in highschool rn and you’re a better teacher then my actual teacher
سبحان الله وبحمده سبحان الله العظيم
استغفر الله العظيم الذي لا إله إلا هو الحي القيوم و أتوب إليه
سبحان الله وبحمده عدد خلقه ورضا نفسه وزنة عرشه ومداد كلماته
اللهم صَلِّ وسَلّمْ عَلَى نَبِيْنَا مُحَمد ﷺ
my teacher is making me watch this
Same
Bruh I'm here because of that too
Ahahhahahha
Same bruh
Same
Its factoring trinomials. The second term(-x) has to found by adding 2 numbers and the third term(-6) has to be found by multiplying the same two numbers. 2+-3=-(1)x and 2x-3=-6, (x+(-3)) and (x+(2)) You can also use the FOIL method on these numbers to go back and solve your original equation. Or you could just use the quadratic equation.
The issue is that you assume we’ve already learned things. No, I haven’t. That’s why I’m here.
Great job! Best math series on RUclips.
I’m in 7th grade learning this and the math teacher did not explain it well enough for me to understand. This video actually explained it well thank you.
That's awesome :)
You're the newest comment I've seen on here too...only 32 minutes ago :3
Dude you keep talking and not explaining. We don't want to watch you doing an exercice, we need step by step explanations.
TOTALLY AGREE!!
I agree! I thought I had it down, but after watching this I am now even more confused. Step by step instructions, please! Do you know of any other video I can watch that would explain how to do this better?
Yes, he is the type of teacher that ends up confusing the student.
If you're don't understand, it means you don't have knowledge in algebra required in order to understand it. Watch previous videos.
He is explaining it very well and clearly, like he always does, you should go and read up on algebra I in order to understand the concepts he is introducing.
The memory refresh thank you
he explains: quadratic equations
I hear: garbage gibberish most complicated explanation
I understand: nothing.
Alaa Faraj me too🙃
Well u have no brain. Im sorry
B1ue 🙃 I don’t think it’s her who has no brain
@@KDizzieI understand him perfectly. It's you racist people who hate Indians that will try yall best to hate.
Indian people dont havr hygiene
I am afraid to say that I see a minor mistake in the polynomial x-squared minus x minus 6. The error lies in the graphing. The parabola's vertex is (1/2, -25/4) not on the y-intercept as you pointed out. The y-intercept is merely where the parabola hits not where the parabola starts. You can find the vertex by using the formula -b/2a.
17 years later, its still complicated and simple at the same time!, crazy!
can't even explain how much I love khan academy.
Thanks Sal you always help make hard things seem so easy.
actually if you solved it along w him, its really easy to understand. just require some basic mathematical understandings like factorization etc. mans doing a good job imo
Your teaching is good
Sal is the best teacher ever
14 years ago's video 😯 now I am 14years old watching this video😐
thanks I'm tryin to prove to my stupid school how smart i am I'm goin to to ahead and learn everything ahead of time I'll be in tenth grade next year learning about geometry and I'll be teaching my teacher about calculus! i bet theyll change their minds and let take the accelerated classes then!
I'm kinda confused...
Me after after the first 2 minutes: I think imma go back to living my life...
I did the same thing right before I found this comment 😂
This video posted before 17 yrs it is older than or equal to me😂
Now iam grade 12 student and watching 👀
a quadratic equation is an equation that inviolves x to the of 2 (x^2) but does not involve x to any greater power (fx: x^3) nor any square roots exponential funktions or any other funky stuff.
quadrtic equations go by the form of f(x) = Ax^2 + Bx + C though you could also write y instead of f(x).
OMG i've never understood anything so much as i did now SUPER THANKS! my math teacher's not that good at teaching :(
16 year later still usefull
I factored -10x^2-9x+1 into (-10x+1)(x+1) and I got the same answer! Thanks Sal!
Help my brain
Bruhh i wasn't born when this relesed
It was before me
same with me, I was born in 2008
I'm amazed that I actually understood that...
14 years later now and i stil struggling with maths but this guy always makes me remember this for a day and then I against start forgetting but remember his wise mathematical words
Thank you I have no idea why it was 0 until you draw the graph :)
Your videos helped me a lot
if you have x-3=0 or x+2=0, you get that because when you are looking to find x, x will ALWAYS be the opposite of what was in the equation. For instance, x+24=0 or x-9=0, x will be equal to -24 and the other x will be equal to +9 because of opposites.
The graph drawn gives an impression that the vertex lies on the y-axis but it is in fact @ (0.5, -6.25). Therefore symmetrical about x=0.5
@idricool teach* most* / all* I hope you become a professor* - Your english teacher has done a very good job.
Still doesn't tell me what a quadratic is..What is a quadratic used for.Why is it important to solve the equation at the root?
exactly.
wait what will this topic do for us in life overall?
MannB did u rly say (BASIC)
Err if you throw a ball obliquely, it's ideal path can be represented by a quadratic. You can find out how far away it will land (y =0) or when you drop a missile, it traces path which can be represented by a quadratic if you don't count in the effect due to air friction etc. So approximately if you solve for Y = 0, you are finding out where it lands
The quadratic equation is used when you don't know (for example) what two numbers add up to get -9 and multiply to get -10. The guy didn't even need to use the quadratic equation he should have multiplied the one by negative 10 and factorised it that way. I was also pretty confused at the end of the video.
Could you please explain each step with more detail work .I watched it twice but didn't understand anything . Thanks in advance .
sameee
@@annaocampo2194 i think we 3 are right brained i never understood anything in math
sorry quadratics confuse me lots at the beginning of the video, can you please explain where the -3 & 2 came from did you divide something? :)
This. This right here is why i could never figure out quadratic equations. This is the complicated video I have ever seen.
Thank you for making Math fun for me, after 20 years of leaving school I decided to go back to school again. I only wish my teachers at school could have made Math so much fun for me as you do. I wish you all the best and hope you continue doing this.
Khan academy i'm in need of you again
>test tomorrow
>slept in class during lesson
>khan saves the day
woah khan academy 13 years ago!!
-10 x 2 = +20? :S
It's a negative multiplied by a positive, which will always be a negative; hence -20. The guy got it right, good video.
Would help if you recommend a previous video to watch if you are confused in what is mentioned in this video
x²+6x-7=0 x=-6/2±√((6/2)²+7)=√16±-3 x#1=1 x#2=-7 pq
x²+6x-7=0 x=(-6±√(6²-4(-7)))/2 = (-6±√(36+28))/2=(-6±√64)2= X#1=1 X#2=-7 I prefer the pq formula instead of the quadratic formula because it has fewer steps to calculate.
Here it is written down x=-(p/2)±√((p/2)²-q) the only problem is when you have a value behind x² so you have to divide that away. Both have their problems.
Very Helpful, Thank you very much!
Woah, this video was made the year I was born
Gah! I am still so confused! :(
same
@@daksharyavanshu7964 *all
@@daksharyavanshu7964 must feel real dumb commenting on an 8 year old comment XD
@@INKY-ONI bruh
@@daksharyavanshu7964 say the guy who not only posted on a 8 year old comment to state that the people are idiots but misspelt all
Awesome video!! Thank you.
Wow this was posted before I was born and I'm watching it now 13 years later
Sweet We are going to learn this in like 6 months, im going to be agead of the game.
agead?
0owh..
n0w i really2 understand it better!!
TQSM!!
u r a great techer^^..
hey grandma can you teach me now? pls if you still remember
Thank you so much teacher
Barrons PSAT/NMSQT 8/9 Study Guide Premium 2023 actually took this first question from Sal. I am currently in the "Passport to advanced math" section, and I got shocked seeing that was Sal's question. Just something I wanted to share with you all. The page number is 419 Question 13.
-10x^2-9x+1........
this could also b done by midlle term splitting .... that method is much easier ;-)
+Videh Patel the idea of the example is to demonstrate the quadratic formula. since it can be also be factored, you are then able to show that the quadratic formula produces the same (correct) solutions. i'm pretty sure he chose a polynomial as his first example that had rational solutions so that he could connect the idea that the solutions are geometrically equivalent to the x-intercepts.
ok... thnx 4 clearing me out
Who's grade9 need to watch this
Wow, what an excellent way to explain the concept of "equal to Zero" in quadratic equations. Thanks!
Thank you so much for doing It
How has this taught me more than 4 hours of uni lectures on this
Sal, you're AWE-SOME. First video and I already understand what's going on. THANKS!
man you speak damn fast. but that doesn't hinder the extremely legendary tutorial!
His „messy“ handwriting is what my handwriting looks like on a good day lol
this is quite simple, love this
Thank you sir 👍 I like the way you explained 👍👍👍👍👍👍
this vid was made before I was born and I'm watching it rn lmfao
who else it watching a ton of vids cause they didnt study in math for online
😅😅meee
This actually easier than you think it is
Double No
triple no
Quadruple No
Yes
Great video, thank you so much.......
13 years later and still complicated
I need help. Every question I do I always end up with a decimal even when i'm not supposed to get one. I JUST DON'T KNOW WHAT I'M DOING WRONG. It happens every time I do a square root.
Check for calculation errors. And use long division
don't use long division, actually. too much room for errors. use a scientific calc or Mathway. (a good site for math)
This isn't "introduction"...
But...
Good work...
can you help me?
it was (x+2)(x+2) = (x+2) times 0 = 0 so either way, if x = -2 then the equation simplifies to 0=0
Spoiler alert
This man helps with any topic of learning in khan academy history
Thanks for all your help. I really like the way you teach. I thumbs up all your videos that helped me. Once again thank you for your help.
The whole F of X confused me a lot but just think of F of X as Y= equation and follow it step by step. Had to watch this twice and it made sense
I’m in grade 3 and you still taught me quadratics
Please put how to factor polnomials using a graph without calculators, just a plain graph and its curves and intercepts :)
EXCELLENT ! SIR IT WAS BRILLIANT
Best video ever
Does it matter if i put -2 and 3 for the factoring ? Does it affect the graph differently ?
I think it does matter
I nearly fell asleep to your voice
Good or bad thing ?
I know, I _really_ have to want to learn something in order to get anywhere with khan academy
So rude
How'd you get " -2 " on 1:07 ... plss answer me man, I really need this.
my though too! +2 x +2 = +4
+Annie Ruth Because when solving for x, x+2=0, you have to minus the 2 from both sides. -2 minus 0 is -2.
I will rewatch it. Thank you,
Negative two because to get rid of +2 they used -2
@@einnaawac You were Annie Ruth but now you are Annie Coager, did you get married? haha
Awesome!!! Thanks for the lesson!