Want to PASS Algebra? You better know this formula 

In high school, I aced algebra. In college, I aced calculus. But it's been over 50 years since those days and I've forgotten a LOT! Thanks for the review.

I was utterly lost 40 years ago when I was trying to learn this. Nothing has changed.

I’m an 8th grader doing pre algebra and I decided I’m going to teach myself algebra and calculus since the school doesn’t want to

I have absolutely no use for quadratic equations at my age and in my situation, but you got me interested enough to look up the history of them. I do remember an algebra teacher that took up (wasted) one entire class period by showing on the blackboard how the quadratic equation was derived. Oh, I should mention that I found your presentation very clear and very useful.

Excellent teacher/instructor. 😊

How many of your students understand what this quadratic equation represents and the relevance of this "answer", or more accurately in this case, these two answers? Without understanding what it is they are trying to solve for, do they realize the possibility of having two, one or even no solutions and why those possibilities exist? I found showing them visually what they are trying to solve for and what the possible results mean made for better understanding of the solutuons they end up with. I had them do a rough graph of their results. It made for a better overall grasp of what it is they're working with.

Thanks....it's fun to get back into algebra..... it's been 50 years for me.

Not exactly a secret, it was first published by محمد بن موسى الخوارزمي Muḥammad ibn Musā al-Khwārazmi in the 9th century! We also get the word algebra from his book الكتاب المختصر في حساب الجبر والمقابلة al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr w'al-muqābala. His Romanised name was Algorithmi from which we get the word algorithm.

y = a(x-h)² + k where h = 1/2(-b/a) and k = -a (h)² + c. a = 3, b = -6 and c = 2 so lets find h and k. h = 1/2(6/3), h = 1 k + -3(1)² + 2 = - 1 y = 3(x-1)² - 1. (prove it: 3(x - 1)(x-1) + 2. 3(x² - 2x + 1) - 1. does in fact give us 3x² - 6x + 2 solve for x x = h ± √(-k/a) x = 1 ± √(1/3) x = 1 ± √(3)/3 or as john shows it x = (3 ± √(3)/3). The 3 before the + or minus term is also divided by 3 so we can "pull it apart" so it is really 3/3 ± √(3)/3 bonus round the y intercept would be 2 the vertex of this parabola is the the set [1, -1] and the x intercepts are [1 + √(3)/3 and 1 - √(3)/3 ] I never could remember the clunky quadratic formula, but the vertex formula I could remember. Of course I only use it if I am sure the quadratic equation can't be solved by factoring.

The quadratic formula can be derived by using the completing the square strategy.

No need for any so-called secret formula: 3x^2 - 6x + 2 = 0 3x^2 - 6x + 3 - 1 = 0 3 * ( x^2 - 2x + 1 ) - 1 = 0 3 * ( x - 1 )^2 - 1 = 0 ( x - 1 )^2 = 1 / 3 x - 1 = + or - sqrt ( 1 / 3 ) x = 1 + or - sqrt ( 1 / 3 )

That’s brilliant to revisit quadratic equations. Can it be solved in this way? (3X-2)x(X-1) that way solution is x=1 or 2/3

Thank you so much. I really appreciate you helping me understand this formula! :)

You said put that into your long term memory. I'm 68 and STILL know it despite never using it since school. Will that do?

Confused as hell 😂🤣😂🤣. Definitely have to rewatch.

I prefer 1 +/- 1/sqrt(3). or 1 +/- sqrt(3)/3. And since everyone should know the decimal value of sort(3), 1.732... , you can get the decimal solution without a calculator in sight.

Bro no way, I am thrilled to try this for first time in 24 years of my life.

Good review after 20-40 years, trying to help granddaughter

Surely you should be starting with BOMDAS / BODMAS ie: Brackets, Of the Power, Multiplication, Division, Add and Subtract. Applying a formula before doing the above is overly complicated when it need not be.

Very clear

MR. TabletClass Math thank you for a fantastic video.

Good evening, genius sir, working out this sum Ans,x=(6+✓60)/6,(6-✓60)/6

I literally don't even know how I got an A in Algebra when this seems so foreign to me. I don't remember any of it. I would literally need to start in Pre-Algebra again and work my way back to here.

there is a factor to take into account.

And I got the pleasure, Pleiades, The Tri Days, Steps, De Mond, we don't put an E

Quadratic equation or completing a square.

If it takes 17 minutes to solve one problem..... I flunked already.

Ok I remember how to do this Though I almost made mist mistake as My Algebra 1 Teacher would say “Watch your signs “ I got a little too over confident But I caught it ..Doing Math is a progression You build on what you have already learned As you progress you will have yo previously learn to do the next problems Simply stated you need the skills you learned in Algebra 1 to be able to do Algebra 2 You will need those skills to do Trig Once you have mastered those skills comes Pre - Calculus or Calculus 1 And you used all those Skills to do A lot More Calculus So you take all those above mention math Classes…You need them to do Calculus…With Calculus The door is open the sky is the limit

You’re the boss my 🎩 thank you 😊

The Quadratic formula or factoring

Thank you 😊💓

I just need numbers to play this game.

Shouldn't the PURPOSE of this ANSWER be illustrated in some form or fashion? I don't understand the ANSWER.

wish you'd explain mathematically why can't factor when numerator has addition or subtraction (as opposed to multiplication or division). You didn't really explain it in your video noting one can't factor in that case.

I can live with the usual interruption when you ask your viewers to subscribe but the adds are really a pain in the quadratic formula, if you get my drift. You should give your viewers a break from commercials once in a while.

This may sound like a stupid question but exactly how do you know to plug in the a-b-c values for the numbers in the original equation? 5:22. Why A squared? why not B squared since B is squared in the Quadratic equation.

Ok ..I got 1 +/- 3 to the -3rd power .. But is that wrong?

I think you should have also mentioned 'Completing the square as a solution', particularly as this is how the quadratic formula was originally derived! In fact, do this to get the solution - very easy. I would also have written the answer as: x = 1 ± 1/√3, which is a very tidy way of expressing it.

That is abc formula only when the D is < 0,

Why exactly cant we do 1+/- sqrt(3)/3?

a = 3 b = -6 c = 2

I appreciate your effort in trying to help students with math - it is so important that all students know that you don't have to be special to do well in math. That being said, I am disappointed that the cornerstone of your lesson is to encourage students to memorize a formula. (It takes very little effort to plug numbers into a formula and it is not very rewarding.) This is absolutely the most destructive approach to learning math and one that turns otherwise intelligent students away from science in general. For god sake, teach them how to develop the quadratic formula. It's basic and any reasonably intelligent student can learn it in short order. Math isn't about blindly memorizing formulas on faith.

It is the formula to solve quadratic equation .for. A 9th class student

Where's the secret ? Uh... Man you're ok ?

This is not any secret formula, it is taught in tenth standerd in India, (SSC Board

15:05 can’t u simplify the 3’s to just leave +- the square root of 3 as an answer?

Quadratic?

2 mistakes in this video. He said a was a variable. In fact a is a constant in this problem. More importantly he failed to point out that a, b & c are coefficients...

Not really. If you give me the formula then would it be still a secret formula.

This is simple quadratic equation he is taking 17 mins to solve thr problem

Your approach is much too slow, repetitious, very tedious, and not necessary.

shhhhh, it's a secret! Don't tell us!!

You have a huge libary? Does your libary, per chance, contain any library books?

Didn’t like it because of no check answer and no explanation .

Are you trying to help or just show how smart you are,you could have slowed down just a bit for those that are not as knowledgeable as you are, for I was very eager to get this but you lost me at the square root of 12, could have explained that part little more indept ,after that I lost my will in frustration to anger to carry on,thanks for getting my hopes up to being more intelligent in mathematical equations only to feel less than .

I think it might be Bertrand Russell who said something similar to: "Education is the art of turning the obvious into something almost incomprehensible."

I haven't seen this in 25 years and was quickly reminded of the formula. To this day, I have yet to find a use for this formula. Doing construction, many calculations are used involving algebra, geometry and some trigonometry, but nothing yet. Oh I remember the days of beating my head against the text book trying to understand. It's great when a coworker asks how much is 200mm and after a slight mental pause, respond with the answer is roughly 8" because they have to allow that much clearance for an electric fireplace. Checking on a conversion calculator, the answer is 7 7/8". That math is important also.

This is all about the so-called abc-formula, very easy when you cannot factor a quadratic equation. It also contains the so-called Discriminant (b^2 - 4ac), which informs you about the 'fractionability' of a quadratic equation (if the D = 0 you can always fraction the equation) and about the kind of the solution ( 2 real numbers, one 'double' solution or also imaginary numbers as solution(s) ).

12:32 you should stress, that you are looking for a number that can be square rooted, therefore not 2x6. In an Example such like a square root of 64, (2^2)(4^2) both can be square rooted and be 8^2, but 2x32 can not be squared for a full number. You should emphasize you're looking for a number that can be squared.

Why didn't you reduce your fraction? The answer I get is: 1 +/- 1/sqrt(3) My Alerbra teacher would've taken off a point or two for not reducing.

my high school math teacher would NOT have given full credit if the answer had not been further simplified, and properly presented as an equation solved for x... x = 1 ± (1/√3) 🤓 .

Can you also explain why this formula is so "secret"? It can be found in every book that has a topic about solving quadratic equations. Please don';t use these kind of qualifications. There is nothing "secret" about that formula.

we just learnt this a week ago 😅

Love ya...you definitely are a BIG HELP...Thank you

Amazing how a 5 minute explanation can be stretched into a longer, more boring explanation than I heard in 60's high school.

This formula is given by an Indian person Sri Dharmachary ji

The Quadratic Formula: To the tune of Row Row Row your Boat: x equals minus b, plus or minus the square root of b squared minus four a c, all over two a.

I loved the thorough, step-by-step breakdown. As a math tutor, I’m definitely going to need it!

the quadratic formula is good to know but this example is easily solved using complete the square.

Your explanation is excelent. Wish I had you as a teacher at school. ( I'm 72 years old) I knew the quadratic formula but Imade so manny mistakes that the result was scrambled eggs in a tumbledryer.

Thank you for the thorough explanation; just too bad others didn't watch the entire video would have eliminated half of the unnecessary comments.

Why not include the significance ie the two points where the graph of the parabola crosses the x axis?

Quit yammering and get to the frappin point!!!!!!!

Hello. Isn’t it easier to first calculate Delta = square b-4ac over 2.a. If Delta is strictly positive there are two solutions then calculate x1= -b-Square root of Delta and x2= -b+square root of Delta. Your formula cumulates all and I think it can lead to errors of calculation. I am French, 76 and very poor in maths!

Great experience, thank you, it can help with heaps of students who do not understand in equations like this! Thank you once again. God bless your online class,

3x^2 -6x +2 = 0 I avoid the quadratic formula where possible. Too much hard work and let's make your brain work. Use complete the square on the LHS. divide it all by 3 (the 'a' part) and put the 'number on the RHS: x^2 -2x = -2/3 take the 'b' part (2), divide by 2 (so = 1 which will be a part of the final square), square it (so = 1) and add that to both sides: x^2 -2X +1 = -2/3 +1 = 1/3 LHS is a square: (x-1)(x-1) = (x-1)^2 = 1/3 so x-1 = plus or minus the square root of 1/3 x = 1 + 1/square root of 3 or 1 - 1/square root of 3. that was done in a few seconds as opposed to > 17 minutes

It is correct that the (3±sqrt(3))/3 can't be simplified to 1±sqrt(3), but it CAN be simplified to 1±(sqrt(3)/3) by first splitting it into (3/3)±(sqrt(3)/3) then simplifying the 3/3 to 1.

This is the standard presentation of the abc-formula. I have a better formula based on this one with a few steps that make you understand parabolas. My formula: x1,2 = xtop PLUS/MINUS delta With xtop = -b / 2a and delta = SQR (D) / 2a and D = b² - 4ac STEP 1 DISCRIMINANT First you work out the discriminant D = b² - 4ac When D > 0 then there are 2 points of the parabola crossing the x-axis When D = 0 then 1 point touching the x-axis (of course this is the top of the parabola) When D < 0 then there are no points crossing the x-axis, the parabola is fully above or under the x-axis In this case: D = (-6)² - 4.3.2 = 36 - 24 = 12 so there are 2 solutions for y = f(x) = 0 STEP 2 XTOP Now we know there are 2 solutions for y=0 we need to calculate the x-coordinate of the top of the parabola: xtop = -b / 2a This formula is part of the original abc-formula. The xtop is very important because the vertical line through xtop is the axis of symmetry of the parabola, so every point of the parabola has the same distance to this axis of symmetry. In this case: xtop = -(-6) / (2.3) = 6 / 6 = 1 STEP 3 DELTA This symmetry is also given for the crossings of the parabola with the x-axis, so the distance of x1 to xtop is the same as x2 to xtop The formula of this similar distance: delta = SQR(D) / 2a In this case: delta = SQR(12) / (2.3) = SQR(2.2.3) / 6 = SQR(3) / 3 STEP 4 SOLUTIONS FOR Y=0 The modified abc-formula: x1,2 = xtop PLUS/MINUS delta So x1 = xtop MINUS delta and x2 = xtop PLUS delta In this case: x1 = 1 MINUS SQR(3)/3 = 3/3 - SQR(3)/3 and x2 = 1 PLUS SQR(3)/3 = 3/3 + SQR(3)/3

a formula without developing it is criminal. You should use krafts to develope the formula. So get out your paper , glue and scissors. Rearrange the standard form quadratic . First make a =1 by dividing all terms by a . We get x^2+(b/a)x +c/a = 0/a=0 The c/a term is a number. Subtract it from both sides of the equation. To get X^2+ (b/a)x = -c/a The left side of the equation consists of a square (x) by (x) and a rect. X by (b/a). Get the scissors out and cut the rectangle lengthwise into 2 equal parts. Now we have a square and 2 rect. (X by b/(2a)) Glue the 2 rectangles to each side of the square. We now have a square x+b/(2a) by x + b/(2a) Area =(X +b/(2a))^2 Well almost. We have overstated by b/(2a) by b/(2a) Area =((b/(2a))^2 We now have a square and an anti square on the left side. The anti square is a number so by adding to both sides of the equation The left side of the equation is a square and the right side is number solve for x in terms of a,b, c you get X= (-b +- (b^2 - 4ac)^1/2)/2a By completing the square.

Actually, you can go a step further by separating this "final answer" into (3/3)±(√3/3) = 1±(√3/3). This is your true final answer.

You could just derive the equation by completing the square.

It should perhaps have been mentioned that if the part SQR(b^2-4ac) is negative. The answer will be a complex number. And in that case it OK to write no solution. At least in entry level algebra classes. Because if you have not learned about complex number, you can not deal with them

Sorry John but did you say that you have a huge LIBARY or LIBRARY. If you said Library, then I would suggest checking on your English grammar and pronunciation notes.

... You also have the " COMPLETING THE SQUARE " method : Given 3X^2 - 6X + 2 = 0 ... X^2 - 2X + 2/3 = 0 ... (X - 1)^2 - 1 + 2/3 = 0 ... (X - 1)^2 = 1/3 ... (1): X - 1 = SQRT(1/3) = SQRT(3)/3 or (2): X - 1 = - SQRT(1/3) = - SQRT(3)/3 ... X1 = 1 + SQRT(3)/3 or X2 = 1 - SQRT(3)/3 ... S = { 1 + SQRT(3)/3, 1 - SQRT(3)/3 } ...

Warning! If you got a prize, a Mac Pro or an IPhone, for getting the right answer you will have to pay several hundred US dollars in International Shipping and Customs fees, and you won't ever get a delivery. If you paid with a credit card you should cancel that card asap.

From square of b Take 4ac Then root extract And b subtract And thereupon Without delay Divide the whole By 2 times a Thanks to the old gent who ran the candy store near my middle school

ok so I looked this equation up on a calculator site since I got a different answer, and it is basically the same, but the 3+-, is 1+ or minus. (The sqrroot3 over 3 is the same)

Actually the correct answer is x = 1 +/- [1/3(3)^1/2]. You need to simply your answer one step further.

Ok so that is your secret formula. When did you discover this formula. Thanks. I like a stupid used to use the quadratic formula. From now on I will use your secret recipe

Did all this crap over 40 years ago.when i look back.what a waste of my time.can someone tell me who this benefits apart from people who teach it.Seems to me how much crap is taught today.that nobody uses.people finishing university with qualifications that nobody wants to employ.

still trying to understand why the answer is not given as 1 plus-minus (sqrt3)/3 thinking it could be just a preference for how the answer is to be presented?

I totally. Loved all you’re stuff but …. SECRET ! …. Dude you taking the piss??”!

I really hate how he goes from working thru a trig problem to explain how to do multiplication. Seriously? Also don't want or need to hear stories about your teaching.

i think thats why i hated math. its not an answer. its not a number! its still an unsolved equation!!! for an answer> and we are told numbers never lie. LOL this says numbers always lie. the square root of 3 is an endless number so you can never get a number out of the equation. this has always boggled my mind. and given me headaches.

The formula is not secret and your presentation that glosses over taking roots or factoring without explanation / amplification with an example is unhelpful. Unfortunately like most of your lengthened first level introductions.

cross cancel?? My high school teacher would go crazy if he heard this. He preferred, "the 2's will Divide out" .

What is simpler, your solution or 1 +/- sq root of 3 over 3? Or am I totally wrong? It's been a long time since algebra 🤣

By completing the square , my answer is 1+_square root of 3 all over 3. Is this correct? Tnx

Dude, in India it is known as shridharacharya formula found long years ago. So keep quiet, we are using since ancient times.

You didn't define what a quadratic equation is & how to identify one. That should have been the basis of your lesson from the beginning.