Why do math teachers in high school never show how to prove stuff. They just say here's the formula now DO MATH. Takes out all the fun out of math. No wonder so little people in my class like it.
i would agree that this is one of many problems. however, every time i would go over a proof while teaching the students would ask: is this on the test? 'No' would almost always be the answer at which point they would stare off into space...
That's an excellent question. I think it's partly in fear of many students falling off, since proofs often are more theoretical and complicated than computing. Second, many teachers simply doesn't have the knowledge to carry out these proofs, and certaintly not with great didactic ideas. However, the beauty of maths lies within deriving such formulas and carrying out proofs, so we are actually too often (and in many countries) teaching computing, not math
I'm watching this for homework as an eighth grader... The teacher says that we have to present it to the class. Pretty interesting, but I'm still kind of "I get it, but where did you even get that idea?"
Misterlikeseverythin not every teacher, my teacher showed us this, but while he was doing it hardly anyone knew what he was doing. Well until the end when everyone was surprised of what had come out (QF).
Amen to that. I have spent the past two years in an engineering school. I love math and physics, but damn, stop handing me formulas to memorize. I have the equipment for this, why do almost none of my professors require this as part of the curricula? It makes my understanding feel so shallow and fake.
Great explanation! In high school I remember deriving this but that's been over 50 years and now I'm teaching my grandchild so I wanted some reminders.
@azk2020 well, often times people want to know why something is true. showing why something is true (some formula) is usually much more difficult than showing how it is used. i think just about everyone has seen the quadratic formula by high school, so i think it is rewarding to know where it comes from : )
Thank you so so much for making this video! I was really confused when my math teacher explained this concept today, but your video has really helped me clear things up.
Genuinely thank you so so so much. I was stressing over this earlier today and now I have no worries about it and I fully understand the concepts. Thank you again.
I am 30 now and this question popped up in my mind while solving 2nd degree polynomial equation without calculator that how this formula arrived. In school and college i didn't have enough time to question my self how this formula arrived. Now I m an electrical engineer in power generation company. Thank you sir that was pretty impressive 👍😊.
Great vid! My math teacher in Algebra 1 my freshman (1989) year had us practice completing the square every day for weeks. After doing the repetitive task several times, I knew there had to be a formulaic way to get the answer. So one evening I went home and figured it out exactly as you showed here. I went to school early the next day to wait for my teacher to get there to show him what I discovered. I was very excited because I thought I was going to get my name on a function that hadn't been discovered yet. He was extremely impressed that I figured it out, and then smiled and had me flip my algebra book ahead a couple chapters to the quadratic formula. While he was excited for me, he totally let the wind out of my sails. Three years later when I was a senior, he wrote an incredible letter of recommendation for me when applying to a university to study Actuarial Science. I got accepted with a very nice scholarship to boot!
The derivative is defined as the limit as h approaches 0, of f(x+h) - f(x) all divided by x+h-x. It is the slope formula except for a point that is infinitesimally close the value of x. If you set h to zero and solve the resulting limit based on f(x). This will then give you the formula for the slope at any point on a curve! It just turns out that this formula always gives the answer of reduce the exponent of n by 1, then multiply by the old exponent. Hope this helps but I'm in grade 11.
Hey, I really want to let you know how great this video was. Maybe I am a weird person for being like this, but I can't bring myself to use stuff in any sort of subject until I know exactly why it is that way so you have definitely helped me understand how the quadratic formula is found and why it makes senses to use it for problems. :D
Awesome vid man! I'm starting Calculus 3 in the spring, and that equation just always seems to keep coming back! lol Now I finally know where that beastly equation came from. Thanks for showin it!
I'm an 8th grader this year and we have to take a test tomorrow over Ax^2+Bx+Cx and finding the quadratic formula. I am SOOOOO grateful for this video!!!😄😄😄
Thank-you so much for this. It was set as homework and I made so many 'silly mistakes' which meant before I watched the video I had spent hours trying to complete it myself. You have 'showed me the light'!
3:24. I keep forgetting what I'm actually needing to add back in! I kept adding b^2/4a^2 to the right side. All the other examples online I found took the a across as the first step so I wasn't able to discover my problem. Thanks! This often catches me during completing the square - neglecting to pay attention to the constant outside the parentheses when deciding what needs added back in.
Thanks so much, Patrick! I'm shamed to say that I never knew that, yet I have a math degree. I never had a clue about how to isolate the x . How on earth could anyone criticize your great presentation? They could look elsewhere if they didn't like yours. I'm a southpaw just like you, and our hands tend to cover what we are writing. I just wanted to see every step shown the second you were writing it. Now I can teach this to my advanced students. Again, thanks so much!!!
After 20+ years of wondering, I finally got focused enough to actually look this thing up. As someone who tries not to take things for granted, this bothered me for decades. But it would only be flashes I would end up ignoring. Today was the day I said: NO MORE! It's fascinating how it all fits perfectly after the "perfect square" gymnastics. Like, the same denominators on both sides made it smooth. Math is magical, too bad I was kind of an idiot in youth and gave up on education
Man, that was awesome! A bit like learning about the creation of the Pythagorean theorem in-so-far-as it's applying known information to make a brand new method that is much simpler and faster to use that can be applied to all equations of that subject area. GREAT EXPLANATION PATRICK!!!
im gonna hv a test next week and this video rly helped, it was actually kinda entertaining (even tho maths is d most boring subjects out there)! now i'll go through all ur other videos ^_^
Man, that was really cool. A bit like learning about the Pythagorean theorem in-so-far-as it's a really interesting way of applying what you already have to come up with a brand new method of working equations in a much simpler and faster way. Great explanation Patrick!
Thanks @patrickJMT this´s a really helpful staff that many teachers miss. Could you make some more videos deriving quadratic formulas? ... like the discriminant, intercept, or the vertex form. It happens that many times they teach you a formula, but you don`t really understand the how did it came, this is a great way to understand math better (Y). Thanks you again.
thank you very muCH! five points bonus on a big test if we could derive the quadratic formula. and believe me those points were much neeeded! thanks again!
yes you make me happy. and I'm not gonna lie, that was confusing, trying to derive stuff in trig right now. Its hard but you explain thing so well. keep going!
I'm always forgetting the exact formula, and it is great to be able to simply derive it.Of course, I had also forgotten how to derive it... oh yeah, completing the square. The cobwebs begin to clear. I appreciate everything you do, Patrick. TFS!
Damn I'm commented on 2019 here lmao. Also Jesus i really suck at math i just wanna say thanks for putting an effort to this video really helps me a lot.
WOW! This is gonna sound like a cheesy testimonial thing, but until I saw this video, I was TOTALLY stumped as to how the constants '4' and '2' got into the quadratic formula. Thank you, Patrick, for making this concept so understandable via RUclips video. As to the person who said Patrick explained it too fast, you can always stop the video, use the round video "counter" to go back to the point where you get stuck, and look at the equation, and think it through for as long as you need to.
I taught my students how to do this by completing the square on 3X^2 + 6x - 12 = 0 . They are proficient at completing the square with numbers at a, b, and c terms. I then put the above mention equation on one side of the white board, and we followed the steps onto ax^2 + bx + c = 0. They were able to quickly understand each step due to their familiarity with completing the square. These are 9th grade freshmen.
Omg thank youuuuuu! I was so confused in this concept! Thank you very much for explaining this! My idiotic book just wrote it directly instead of explaining the points 😭😭😭 Finally I understand :'D
thanks for making this video...its helps a lot for cause as far as I know deriving the quadratic formula is actually, one of the question on the Engr board exam.
That was really cool! I always thought this fella just went,”I’m gonna find something that works for all quadratic equations” and ta da he does. At least that was what I thought
my algebra teach came up with a genius way to memorize the formula. here it is: the negative boy (-b) was confused (+ or -) if he wanted to go to a radical party ( the square root box). the boy felt like a square ( b squared) because he missed out on four Awesome Chicks ( -4AC) the party ended at two a.m. (2A). if you put that in the order of the formula you will see it corresponds
Great explanation and some wonderful moves on the maths. I ve been trying to derive this for myself on and of for over fifty years ; so you can imagine how helpful this was - I can do it and I understand it (thanks)^2
this one is a little bit simpler ax²+bx+c=0 shift c to right side ax²+bx=-c divide both sides by a x²+bx/a=-c/a or x²+(b/a)x=-c/a Add (1/2*coefficient of x)² on both sides x²+bx/a+(b/2a)²=(b/2a)²-c/a x²+2(x)(b/2a)+(b/2a)²=b²/4a²-c/a [(x)+(b/2a)]²=(b²-4ac)/4a² take square root on both sides x+b/2a=±sqrt(b²-4ac)/2a shift b/2a x=-b/2a±sqrt(b²-4ac)/2a OR x=[-b±sqrt(b²-4ac)]/2a hope this clarifies
+Daniel Coto bx/a is the same as (b/a)x because if you really think about it, it's (b/a)(x/1). When you multiply fractions, you multiply the numerators together and the denominators together, so (b/a)(x/1) then equals bx/1a. You can then cancel the 1 out from the denominator as a*1=a. You now have bx/a. I do have a simple question though: If you don't know this, why are you watching a video on how to derive the quadratic formula?
There is even more simple intuitive proof. Middle part is sum and last part is product. So S=b/a, P=c/a now you have sum and product, you can calculate both routes. Say your routes are R1 and R2. Do not substitute R1 = S- R2 you will again end up in quadratic equation. Instead, use this formula. (R1-R2)^2 = R1^2 + R2^2 - 2*R1*R2 = (R1 + R2)^2 - 4* R1*R2 = S^2 - 4P Square of Difference = square of Sum - 4times Product Difference D= sqrt ( S^2 - 4*P ) Now we have difference and sum so solution is R1 = (S+ D)/2 R2 = (S-D)/2 Substitute S and D, you get answer. So basically you know Sum and Product, so calculate Difference and u are done (a+b)^2= a^2 + b^2 + 2ab (a-b)^2 = a^2 + b^2 - 2ab R1
on the first step wouldnt it be a ( x^2 + b/a + c/a) = 0 ? because if u leave out the c and move it to the right side of the equation (like you did) the formula wouldn't work if A was equal to 0 although we would get the correct answer: the quadratic formula at the end. just a question i had in my mind
It is assumed that a isn't 0. Otherwise it's not a quadratic equation, because then there would be no x^2 term and it would simply be of the type bx+c=0, which is a linear equation
Thank you for this very helpful video. I have a BEng in electronic engineering, as well as twenty years work experience in IT, working for many top organisations, mostly investment banks but also Microsoft and other 'blue chips'. However, found very poor mathematics teaching, in particular, decent work-throughs and explanations like this. Well done and keep up the good work! Will contribute something next time I have a little spare cash (-;
Divide by a after writing the second line, it makes the whole thing a lot simpler than waiting till later to divide by a. We can do this since a is not 0.
This almost drove me insane. I was trying to derive the formula myself and ran into difficulties after I’d completed the square. I then looked up how others did it to see if I was on the right track and watched this video. Normally, this teacher’s work is great but here there’s a slip in the 3rd line of CTS step. The 4a on the rhs denominator should be squared. This really affects the following steps. And it doesn’t work out unfortunately. Patrick, I really like your channel and recommended it for many years but you really need to post a correction for this as it’s misleading somewhat. Appreciate your work genuinely. Thanks. Mike
D is the discriminant, the bit under the route. D can take 3 types of values: D > 0, so you get 2 distinct roots. D = 0, so you get 1 root (or 2 equal roots technically) D < 0, so you get no roots (or 2 complex roots technically) It only makes sense to write D = k^2 if D > 0. Then the equation simplifies slightly to x = [ -b + / - k ] / [2a]
An excellent video explaining the derivation of the quadratic formula. I followed it quite easily but at approximately the 6 minutes mark I expected when you took the square root on the right of the formula that the b squared would become just "b" rather than being left alone - Is this because the - 4ac isn't squared also?
Why do math teachers in high school never show how to prove stuff. They just say here's the formula now DO MATH. Takes out all the fun out of math. No wonder so little people in my class like it.
i would agree that this is one of many problems. however, every time i would go over a proof while teaching the students would ask: is this on the test? 'No' would almost always be the answer at which point they would stare off into space...
That's an excellent question. I think it's partly in fear of many students falling off, since proofs often are more theoretical and complicated than computing. Second, many teachers simply doesn't have the knowledge to carry out these proofs, and certaintly not with great didactic ideas. However, the beauty of maths lies within deriving such formulas and carrying out proofs, so we are actually too often (and in many countries) teaching computing, not math
I'm watching this for homework as an eighth grader...
The teacher says that we have to present it to the class.
Pretty interesting, but I'm still kind of "I get it, but where did you even get that idea?"
Misterlikeseverythin not every teacher, my teacher showed us this, but while he was doing it hardly anyone knew what he was doing. Well until the end when everyone was surprised of what had come out (QF).
Amen to that. I have spent the past two years in an engineering school. I love math and physics, but damn, stop handing me formulas to memorize. I have the equipment for this, why do almost none of my professors require this as part of the curricula? It makes my understanding feel so shallow and fake.
I can't believe I was never taught this. Thank you, puts some meaning into the formula.
happy to help out. i didn't pay any notice til after i was done with actually taking classes myself
You’re lucky you don’t have to remember it
Great explanation! In high school I remember deriving this but that's been over 50 years and now I'm teaching my grandchild so I wanted some reminders.
THANK YOU THANK YOU THANK YOU A MILLION TIMES!!! THIS WILL BE ON MY MATH FINAL EXAM TOMORROW!!!!! I CANNOT THANK YOU ENOUGH!!!!!!!
Killian Defaoite don’t leave us hangin what’d you get on it?
we're dying to know how it went killian
How was the exam? 😂
@@NellLiuNini Lol. Don't remember.
@@KillianDefaoite The lad finally responded, and basically hit us with an "IDK"
Omg thank you! I started giggling when it all worked out
@azk2020 well, often times people want to know why something is true. showing why something is true (some formula) is usually much more difficult than showing how it is used. i think just about everyone has seen the quadratic formula by high school, so i think it is rewarding to know where it comes from : )
aww thanks : )
glad i am able to help a bit
well, completing the square is basic high school algebra...
i think most any decent hs algebra student could follow this
Facts
True.
Love from India 🇮🇳.
@@vickyyadav_8858 only person here from India bro 😎
I am Indian too
(Actually finding any Indian )
Feeling like done a great job or something great 😊
Thank you so so much for making this video! I was really confused when my math teacher explained this concept today, but your video has really helped me clear things up.
u are a very good tutor...keep it up
The question suddenly came into my mind as to where the quadratic equation driven from, just go to you tube and find you there. Awesome! Thank you.
Genuinely thank you so so so much. I was stressing over this earlier today and now I have no worries about it and I fully understand the concepts. Thank you again.
Deriving is the best lesson for me ,I love to deriving in mathematic.
You might be really good at math, but with that grammar, you should probably worry about your English grade.
@@cotton_flowers and you should worry about your extremely high patheticness
I am 30 now and this question popped up in my mind while solving 2nd degree polynomial equation without calculator that how this formula arrived. In school and college i didn't have enough time to question my self how this formula arrived. Now I m an electrical engineer in power generation company. Thank you sir that was pretty impressive 👍😊.
Great vid! My math teacher in Algebra 1 my freshman (1989) year had us practice completing the square every day for weeks. After doing the repetitive task several times, I knew there had to be a formulaic way to get the answer. So one evening I went home and figured it out exactly as you showed here. I went to school early the next day to wait for my teacher to get there to show him what I discovered. I was very excited because I thought I was going to get my name on a function that hadn't been discovered yet. He was extremely impressed that I figured it out, and then smiled and had me flip my algebra book ahead a couple chapters to the quadratic formula. While he was excited for me, he totally let the wind out of my sails. Three years later when I was a senior, he wrote an incredible letter of recommendation for me when applying to a university to study Actuarial Science. I got accepted with a very nice scholarship to boot!
The derivative is defined as the limit as h approaches 0, of f(x+h) - f(x) all divided by x+h-x. It is the slope formula except for a point that is infinitesimally close the value of x. If you set h to zero and solve the resulting limit based on f(x). This will then give you the formula for the slope at any point on a curve! It just turns out that this formula always gives the answer of reduce the exponent of n by 1, then multiply by the old exponent. Hope this helps but I'm in grade 11.
@iamcool1908 ha, most people are nice, but it is the internet, you can not please everyone all the time! glad you like it though!
Hey, I really want to let you know how great this video was. Maybe I am a weird person for being like this, but I can't bring myself to use stuff in any sort of subject until I know exactly why it is that way so you have definitely helped me understand how the quadratic formula is found and why it makes senses to use it for problems. :D
Awesome vid man! I'm starting Calculus 3 in the spring, and that equation just always seems to keep coming back! lol Now I finally know where that beastly equation came from. Thanks for showin it!
how old are you now?
are you even alive?
I'm an 8th grader this year and we have to take a test tomorrow over Ax^2+Bx+Cx and finding the quadratic formula. I am SOOOOO grateful for this video!!!😄😄😄
no problem!!
just make sure you understand the process, then be careful with all the fractions!
good luck!
Thanks a lot. I've got a quiz on this tomorrow, and this is just what I needed.
Thank-you so much for this. It was set as homework and I made so many 'silly mistakes' which meant before I watched the video I had spent hours trying to complete it myself. You have 'showed me the light'!
Thanks for making this video! I have a quiz on this today so this really helped me out!
3:24. I keep forgetting what I'm actually needing to add back in! I kept adding b^2/4a^2 to the right side. All the other examples online I found took the a across as the first step so I wasn't able to discover my problem. Thanks! This often catches me during completing the square - neglecting to pay attention to the constant outside the parentheses when deciding what needs added back in.
Yup even I did that mistake
Thanks alot for this, your probably the best teacher teacher on youtube and the you would own the math teachers at my school!
Thanks so much, Patrick! I'm shamed to say that I never knew that, yet I have a math degree. I never had a clue about how to isolate the x . How on earth could anyone criticize your great presentation? They could look elsewhere if they didn't like yours. I'm a southpaw just like you, and our hands tend to cover what we are writing. I just wanted to see every step shown the second you were writing it. Now I can teach this to my advanced students. Again, thanks so much!!!
always happy to help out a super star
Thanks so much! I've been wondering for over 15 years how this was done but never set out to find out, until now with your wonderful video! ;)
Thanks for this helps in our school the teachers never teach prove (examination point of view) but I really am thankful to you for this
From class 10 cbse
Really helped a lot sir
Great explanation
From India 🇮🇳
After 20+ years of wondering, I finally got focused enough to actually look this thing up. As someone who tries not to take things for granted, this bothered me for decades. But it would only be flashes I would end up ignoring. Today was the day I said: NO MORE!
It's fascinating how it all fits perfectly after the "perfect square" gymnastics. Like, the same denominators on both sides made it smooth.
Math is magical, too bad I was kind of an idiot in youth and gave up on education
that‘s why i love math，math is beautiful
Man, that was awesome! A bit like learning about the creation of the Pythagorean theorem in-so-far-as it's applying known information to make a brand new method that is much simpler and faster to use that can be applied to all equations of that subject area.
GREAT EXPLANATION PATRICK!!!
I remember how cool it was in 7th grade to go though this in my math class. This brought back such a great memory.
This is a life saver, this is in my test tomorrow tysm!!!
im gonna hv a test next week and this video rly helped, it was actually kinda entertaining (even tho maths is d most boring subjects out there)! now i'll go through all ur other videos ^_^
Absolutely delicious! A very smooth and easy to understand approach.
have a test on this tomorrow and need to have this memorized... wish me luck
@rose quartz yh so how'd it go?
Samee XD
@@dinogaming3145 lol
Excellent explanation. Patient and thorough. Understood it first time round. Thank you.
excellent! just complete the square and be careful with all the letters floating around
Thanks for reminding me. I've forgotten that we had to do that in algebra. Very useful.
Man, that was really cool. A bit like learning about the Pythagorean theorem in-so-far-as it's a really interesting way of applying what you already have to come up with a brand new method of working equations in a much simpler and faster way.
Great explanation Patrick!
I love this video. I have to memorize how to do this and your video is very well explaining and makes it a lot easier to remember. Thank you.
@geraoma you are very welcome : )
Very well explained i love watching derivations
Thanks @patrickJMT this´s a really helpful staff that many teachers miss. Could you make some more videos deriving quadratic formulas? ... like the discriminant, intercept, or the vertex form. It happens that many times they teach you a formula, but you don`t really understand the how did it came, this is a great way to understand math better (Y). Thanks you again.
EXCELLENT Teaching.....
Hallmark!....wow!.....
Thanking you Sir.
.From India.
But we Indians feel difficulty in understanding slung Anerican..
Literally searching to find Indian people here
from 🇮🇳 India
thank you very muCH! five points bonus on a big test if we could derive the quadratic formula. and believe me those points were much neeeded! thanks again!
Thank you so much!
I have a test tomorrow and I KNOW this is a question!
THANKS!!
yes you make me happy.
and I'm not gonna lie, that was confusing, trying to derive stuff in trig right now.
Its hard but you explain thing so well. keep going!
I'm always forgetting the exact formula, and it is great to be able to simply derive it.Of course, I had also forgotten how to derive it... oh yeah, completing the square. The cobwebs begin to clear.
I appreciate everything you do, Patrick. TFS!
Damn I'm commented on 2019 here lmao.
Also Jesus i really suck at math i just wanna say thanks for putting an effort to this video really helps me a lot.
WOW! This is gonna sound like a cheesy testimonial thing, but until I saw this video, I was TOTALLY stumped as to how the constants '4' and '2' got into the quadratic formula. Thank you, Patrick, for making this concept so understandable via RUclips video.
As to the person who said Patrick explained it too fast, you can always stop the video, use the round video "counter" to go back to the point where you get stuck, and look at the equation, and think it through for as long as you need to.
Bro thank you so much I'm taking a math test at home right now and this is question 7 of it
I taught my students how to do this by completing the square on 3X^2 + 6x - 12 = 0 . They are proficient at completing the square with numbers at a, b, and c terms. I then put the above mention equation on one side of the white board, and we followed the steps onto ax^2 + bx + c = 0. They were able to quickly understand each step due to their familiarity with completing the square. These are 9th grade freshmen.
Thanks man. I needed to know this for my Geo class
thanks for the useful comment
Thanks very much. Was looking for something like this all over
Thank you sir 🙏my age is 13 years and u am watching it after 13 years whole concept clear .
Omg thank youuuuuu! I was so confused in this concept! Thank you very much for explaining this! My idiotic book just wrote it directly instead of explaining the points 😭😭😭
Finally I understand :'D
thanks for making this video...its helps a lot for cause as far as I know deriving the quadratic formula is actually, one of the question on the Engr board exam.
That was really cool! I always thought this fella just went,”I’m gonna find something that works for all quadratic equations” and ta da he does. At least that was what I thought
Love it. Very concise and easy to follow.
my teacher is trying to make me solve for this during middle school while everyone else here is in high school
Same
my algebra teach came up with a genius way to memorize the formula. here it is: the negative boy (-b) was confused (+ or -) if he wanted to go to a radical party ( the square root box). the boy felt like a square ( b squared) because he missed out on four Awesome Chicks ( -4AC) the party ended at two a.m. (2A).
if you put that in the order of the formula you will see it corresponds
@VIR092 i like it too : )
MAAAAANNNN YOU JUST SAVED MY LIFEEEE. THANK YOUUUUUUUUUUUUU
I missed school when my teacher explained this, so I'm really glad I found this video. Especially since it's gonna be on a test.
Cheers mate, your a lot more better then my Scotish teacher, (i am currently doing year 11extension)
Great explanation and some wonderful moves on the maths. I ve been trying to derive this for myself on and of for over fifty years ; so you can imagine how helpful this was - I can do it and I understand it (thanks)^2
Oh my gosh, thank you sooooo much. I was stuck for so long in Algebra 2!
Juell Towns too bad we have to learn this in algebra 1
Thanks for the cool demonstration of how the quadratic equation came to be. I saw it in class today and was dumbstruck at its emergence. Math is fun!
this one is a little bit simpler
ax²+bx+c=0
shift c to right side
ax²+bx=-c
divide both sides by a
x²+bx/a=-c/a
or x²+(b/a)x=-c/a
Add (1/2*coefficient of x)² on both sides
x²+bx/a+(b/2a)²=(b/2a)²-c/a
x²+2(x)(b/2a)+(b/2a)²=b²/4a²-c/a
[(x)+(b/2a)]²=(b²-4ac)/4a²
take square root on both sides
x+b/2a=±sqrt(b²-4ac)/2a
shift b/2a
x=-b/2a±sqrt(b²-4ac)/2a
OR x=[-b±sqrt(b²-4ac)]/2a
hope this clarifies
***** I can't teach you basic fractions...write it down and try to figure it out..it's hard to tell sth through comments
+Daniel Coto
bx/a is the same as (b/a)x because if you really think about it, it's
(b/a)(x/1). When you multiply fractions, you multiply the numerators together and the denominators together, so (b/a)(x/1) then equals bx/1a. You can then cancel the 1 out from the denominator as a*1=a.
You now have bx/a.
I do have a simple question though: If you don't know this, why are you watching a video on how to derive the quadratic formula?
I don't know if anyone has said this, but deriving the quadratic formula is a CSET question. Thanks for explaining it!
nope, no one has ever said that :)
haha. Well, I gotta say, very well done, sir.
Thanks for a very detailed derivation.
I was taught a method where you started by dividing out the coefficient a, we didn't use factoring except in one or two steps but great tutorial :3
There is even more simple intuitive proof. Middle part is sum and last part is product. So S=b/a, P=c/a now you have sum and product, you can calculate both routes. Say your routes are R1 and R2. Do not substitute R1 = S- R2 you will again end up in quadratic equation.
Instead, use this formula.
(R1-R2)^2 = R1^2 + R2^2 - 2*R1*R2
= (R1 + R2)^2 - 4* R1*R2
= S^2 - 4P
Square of Difference = square of Sum - 4times Product
Difference D= sqrt ( S^2 - 4*P )
Now we have difference and sum so solution is
R1 = (S+ D)/2
R2 = (S-D)/2
Substitute S and D, you get answer.
So basically you know Sum and Product, so calculate Difference and u are done
(a+b)^2= a^2 + b^2 + 2ab
(a-b)^2 = a^2 + b^2 - 2ab
R1
Thanks, understanding the logic is super helpful
Dayumnnn! This is legit cool explanation!
THANKS MAN!
on the first step wouldnt it be a ( x^2 + b/a + c/a) = 0 ? because if u leave out the c and move it to the right side of the equation (like you did) the formula wouldn't work if A was equal to 0 although we would get the correct answer: the quadratic formula at the end. just a question i had in my mind
It is assumed that a isn't 0. Otherwise it's not a quadratic equation, because then there would be no x^2 term and it would simply be of the type bx+c=0, which is a linear equation
@@MultiSuperGuide oh, thanks
Does using the quadratic formula cause extraneous solutions?
when you completed the square why did you add b^2/4a^2 to the left side but on the right side the 4a isn't squared? shouldn't they be the same?
great demonstration man.
Thank you for this very helpful video. I have a BEng in electronic engineering, as well as twenty years work experience in IT, working for many top organisations, mostly investment banks but also Microsoft and other 'blue chips'. However, found very poor mathematics teaching, in particular, decent work-throughs and explanations like this. Well done and keep up the good work! Will contribute something next time I have a little spare cash (-;
Divide by a after writing the second line, it makes the whole thing a lot simpler than waiting till later to divide by a.
We can do this since a is not 0.
yaa! : )
Thank you bro...This video is very useful and easy to me..so again thank you☺☺
Love this video!
love you, burrito!
It is so abstract.This is not what I needed.
love your videos
This almost drove me insane. I was trying to derive the formula myself and ran into difficulties after I’d completed the square. I then looked up how others did it to see if I was on the right track and watched this video. Normally, this teacher’s work is great but here there’s a slip in the 3rd line of CTS step. The 4a on the rhs denominator should be squared. This really affects the following steps. And it doesn’t work out unfortunately.
Patrick, I really like your channel and recommended it for many years but you really need to post a correction for this as it’s misleading somewhat. Appreciate your work genuinely. Thanks. Mike
This was superb. Thank you.
Thank you. It was very well explained. Got extra credit points because of this! :D
Thanks! This is very helpful for us student.
Amazing! Now i have another question
Why is b²-4ac=D=k²
What is D? What is k?
D is the discriminant, the bit under the route.
D can take 3 types of values:
D > 0, so you get 2 distinct roots.
D = 0, so you get 1 root (or 2 equal roots technically)
D < 0, so you get no roots (or 2 complex roots technically)
It only makes sense to write D = k^2 if D > 0.
Then the equation simplifies slightly to x = [ -b + / - k ] / [2a]
wait if you multiply, don't you add exponents? or in this case when it is b^2/4a^2, when you multiply the a, wouldn't it be 4a^3?
An excellent video explaining the derivation of the quadratic formula. I followed it quite easily but at approximately the 6 minutes mark I expected when you took the square root on the right of the formula that the b squared would become just "b" rather than being left alone - Is this because the - 4ac isn't squared also?
Thanks man, helped a lot.