Want to PASS Algebra? You better know this formula

TabletClass Math:


Math Notes:

[fredchristiansen]

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.

[prodkerstii]

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

[quabledistocficklepo]

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.

[fyrman]

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.

[epesooula]

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,

[JeffTheGent]

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

[johannpreiss]

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.

[Kleermaker]

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) ).

[soniacruz]

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

[ivansoup-hales]

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

[SoManyDogs]

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

[axeblue]

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.

[jwacio]

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.

[williamfuller]

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.

[reginemanley]

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!

[stricklandgarageaviation]

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

[christianemden]

In germany it’s taught in a slightly different notation x^2 + px + q =0 solves as x = -(p/2) +/- sqrt((p/2)^2 -q). Learned this in about eighth grade, but have admit since i didn’t use it in a few years i got rusty. Personally i think the notation is slightly easier to remember than your version, but naturally that is all a question of personal opinion.

[nickcellino]

The method shown here using the Quadratic Equation Formula is best because the question is fill-in-the-blank. However, if it were a multiple choice question as on the SAT test, the fastest, easiest method is Sums and Products.

Step 1: Simplify the quadratic equation into x² - 2x + 2/3 = 0 by dividing both sides by 3.

The sum of the roots is always the coefficient for x with the sign reversed. Here this is 2. The product of the roots is always the constant which here is 2/3.

Step 2. Among the 5 choices, determine which choice has roots equal to 2/3 when multiplied or 2 when added. If there are no duplicates, that's the right choice.

Here multiplying the root choices that contain square roots might be easier using the axiom (a + b) x (a - b) = a² - b². The numerator is 6 and the denominator is 9 which is equal to 2/3.

The Quadratic Equation Formula should be a last resort used only when all easier methods like factoring, completing the square and Sums and Products fail or are too difficult.

[Queenofdestruction]

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

[v-gc]

Impressive detailed explanation. Very very helpful. Thanks