Hi, so I’ve seen the quadratic formula in American media being taught like this:
[-b ± √(b2 – 4ac)]/2a
(copied from Google, hope it doesn’t get messed up)
Is this how you learned it? Bc honestly at first I wasn’t even sure what it was supposed to be.
Everyone I know from my country (Poland) is taught like this:
Δ = b² – 4ac
x1 = (-b + √Δ) / (2a)
x2 = (-b – √Δ) / (2a)
I just though it was an interesting difference, and I want to ask ya’ll how were you taught? Is there differences between regions? Or levels of education? Which one seems easier to remember/use?
Comments
First one, we avoid it at all costs
Yes, I learned it the first way you posted it.
First one. NEVER used it for anything.
The first way was the way I was taught it many years ago. Also we had a song we used to memorize it to the tune of “Jack in the box.”
The……what? Never seen this before in my life.
Yes, the one you copied from Google is definitely how I learned it!
I was taught negative b plus or minus the square root of b squared minus four AC all over 2a. I genuinely cannot remember what any of those variables are supposed to be or what the quadratic equation does, but I definitely remember the formula lol. In my defense I graduated high school 20 years ago and haven’t really done high level math since then.
I was taught the 2nd on in Massachusetts
First one is the only one I have ever known. Our teacher even had a song to the tune of “Jingle Bells” to teach us the formula.
Yup. That’s right. We even learned a little song as a mnemonic device.
I was taught more like the first way. Except it looked like this.
[-b ± √(b2 – 4ac)]
2a
I remember it this way because my teacher sang it to us with the pop goes the weasel melody.
The first one is how we learn it.
I was taught the first one and my math teacher even had us sing it.
Negative b plus or minus square root of b squared – 4ac all over 2a.
Your first example seems more familiar.
Even though my job involves a fair amount of math, I haven’t used the quadratic formula since I graduated college in 1979.
Yes, that’s the formula we’re taught. I still have it memorized. You’re expected to know that the ± means you have up to two possible roots.
I don’t remember. I never used it after I learned it to pass the class.
I was taught the first one. From what I recollect, I think I learned it in trigonometry? I don’t remember seeing a delta until the beginning of calculus or maybe toward the end of precalc.
First one. I grew up in US.
Yeah I learned it the American way, we would rarely write it out as x1 and x2. We do technically learn that the discriminant is b^2-4ac but it often gets forgotten. We definitely don’t call it delta, we don’t really have a symbol for it.
We’re taught the first way.
I don’t mind your way of showing it. I think what bothers me is the reddit formatting lol. If you put the “x2” equation on a new row, then it all lines up nicely and is easy to read.
HS math teacher here. I’ve always taught it the first way, but I learned the 2nd way from my foreign exchange students. One of them kept asking me when we were going to learn about delta and I had no idea what they were talking about so I asked them to show me. I like the 2nd way better, but I continued teaching it the first way because I knew that is how it would be presented in their future math classes.
>[-b ± √(b^(2) – 4ac)]/2a
This is the way it is presented in virtually all American math books. The reason is because, by learning that a, b, and c are the coefficients of the quadratic polynomial, you can go directly to calculating the solution without any other steps.
>Δ = b² – 4ac
Be giving the quantity b² – 4ac a special name (Δ), I suspect that this approach is used to reinforce the idea that b² – 4ac is the discriminant, i.e. the quantity that determines whether a quadratic equation will have two distinct real roots, one repeated real root, or no real roots. American math books simply define the discriminant as b² – 4ac without giving it a special symbol like Δ.
Of course, both approaches are fully equivalent.
Both versions are equivalent, but inferior to the method of completing the square
I definitely never learned the first one
Always the first, which is just a more elegant way of displaying the second.
First one for me. It’s been over 3 decades and I can still remember that formula.
I know the first one and use it relatively frequently because I’m an engineer. The second way would be annoying to me because it’s less compact. AFAIK we only use the shorter notation for the most part.
I was taught the first one that you copied from Google. I have actually used this in my work multiple times. I calculate the square root term and then use that in both the plus and minus calculations rather than re-doing the square root each time.
The first one. In the US, we almost always use delta (Δ) to indicate change or difference (e.g., “What’s the cost delta between option 1 and option 2?”).
I was never taught such a thing or what it would be used for, but I didn’t major in anything math focused in university.
I didn’t learn it till I was 30, but yup. X is equal to the opposite of B, plus or minus the square root of B squared, da,da,da
They’re the same thing. Your method pulls the +- apart into two separate equations and used a variable for under the radical. Breaks it into smaller bites making it easier to use.
I’ve never seen a formal symbol for just the discriminant even though we refer to it separately when applicable. I remember my algebra teacher presenting the proof for the quadratic formula, but the formula was presented as the entire ratio with the discriminant rather than a separate formula for the discriminant.
It’s been 30 years, but I know I learned the quadratic formula, and I always did good in math, even through AP calculus but this doesn’t look familiar at all lol.
Guess it’s true, use it or lose it.
I don’t even remember what that is let alone how we learned it 😂
Yes, but then we spend way more time on factoring polynomials.
Yes but many students would work it like you have it to find the determinate first as that indicates whether you have 2 ,1, or zero roots
From what I remember, there might be a passing mention that b² – 4ac is called the “discriminant”, but there is little to no focus on calculating the discriminant separately and determining the number of roots. Instead, the quadratic formula is taught in the longer form you mentioned, students plug the numbers in, and their hand calculations (or calculators) spit out a result.
We learned the first way to calculate the quadratic formula. We also learned about the discriminant (your Δ = b² – 4ac) and how its values change the type of results that can be expected from the quadratic equation.
This was Algebra II, sophomore year (15-16 year olds), at an American high school in Germany at a US army post.
Doesn’t matter to me, I couldn’t ever remember formulas. I can do the math. Just why do I have to remember this.?…my 40 year old angst just bubbled up. Sorry
Yes. I teach Algebra and my students don’t even have to memorize it. It is available on their state test reference sheet.
Math is universal, but I’ve learned there are a lot of ways to get to the same answer. I teach kids from all over the world and it’s pretty interesting to see different ways that kids know how to solve problems.
Yup differences in teaching paradigms:
American schools are focused on route memorization and regurgitation so we’re taught one formula because it’s easier to memorize.
European schools like their students to have a greater understanding so they break it into two equations and make the student “build” the solution.
In my opinion the European model is better.
I was taught to memorize it the first way, but we were introduced to it by deriving it from ax ^2 + bx + c = 0
Learned it the first way. We also learned a mnemonic for it to the tune of Frere Jacques
Alex, I’ll take math I haven’t used in 30 years for $200.
This is definitely one of those things I learned, then disregarded immediately after testing because I already knew it would never prove useful to my life.
Here I am, 12+ years later, and I was right.
Haven’t thought about that since high school which was 23 years ago and still dont know what it does or what we used it for. All those math classes I starred off into space and thought “I’m never going to use this” were correct
I was taught the first way. We were taught it as a rap. So now I can only remember the quadratic equation by rapping it. But I do still remember it!
the quadratic formula is in fact what you posted, and how we are taught to commonly solve the formula is how you were taught in poland.
The version you copied from Google is how I learned it in 8th or 9th grade way back in 1983 or 1984. I remember memorizing the phrase: “negative b plus or minus the square root of b squared minus four ac, all divided by two a”.
You learn to the the tune of either Pop Goes the Weasel or Don’t Stop Believing.
That’s how I learned it in California. I had no idea there even was a different way until your post.
Your way does make sense, but seems slightly more complicated to write out.
First one.
I definitely remember that THING
We are not all taught it at all.
I actually learned about it right here, in this very reddit post.
Yes. We even had a song to the tune of Pop Goes the Weasel that sang that formula.
My husband, who is Asian Indian, but grew up in North Africa, learned the top one.
I was taught to start with a generic polynomial ax^2 + bx + c = 0 and then complete the square which gives you the quadratic equation you initially posted.
Americans would learn about properties of the discriminate even if they don’t represent it with delta.
I learned it with a song.
X=[-b ± √(b2 – 4ac)]/2a
This is how I learned it.
We memorized it in song form to the tune of pop goes the weasel.
X equals negative B (All around the mulberry bush)
Plus or minus sqaure root (The monkey chased the weasel)
B squared minus Foour AC (The monkey thought ’twas all in fun.)
All over Two A (Pop! Goes the weasel)
I’m not sure if everyone learned that but for years I know my friends sang it when they had to use it.
I learned it the American way (here in America), and I must say I like it that way, because it makes simplification so much more efficient.
That said, the way you were taught works too, even if less efficient.
I memorized to the tune of Pop Goes the Weasel.
“x equals negative b, plus or minus square root: b-squared minus 4ac, ALL over 2a!”
Thank you, Mrs. Schad, if you ever read this!