The simpler quadratic formula | Ep. 1 Lockdown live math

Another view on the quadratic formula.

Beautiful pictorial summary by @ThuyNganVu:

Po Shen Loh on quadratics:

Welch Labs on imaginary numbers:

Mistakes (there will always be mistakes):
At minute 22, I write "b' / 2" instead of "-b' / 2".

Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld

------------------
0:00 - Introduction
2:56 - "How often am I going to use this?" + ray tracing example
5:38 - Mental math tricks (factoring numbers, differences of squares)
13:36 - Properties of quadratic functions
18:40 - Deriving the variant quadratic formula
23:07 - Practice problems (ft. complex numbers!)
34:10 - Deriving the traditional quadratic formula from the variant
41:07 - Conclusion (key takeaways)
43:21 - Fun with joke poll questions
------------------

Music by Vincent Rubinetti.
Download the music on Bandcamp:

Stream the music on Spotify:

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.

------------------

Various social media stuffs:

[michaelscofield]

How does he sound so perfect even though it's live, he doesn't stutter at all

[Galenus]

This human sounds like the talking animated pi on youtube. How curious...

[bowtangey]

After 30+ years of university teaching I see that I haven't thought deeply enough about the multiplying of two numbers. Fantastic!

[dsfridley]

0:00 - Introduction
2:56 - "How often am I going to use this?" + ray tracing example
5:38 - Mental math tricks (factoring numbers, differences of squares)
13:36 - Properties of quadratic functions
18:40 - Deriving the variant quadratic formula
23:07 - Practice problems (ft. complex numbers!)
34:10 - Deriving the traditional quadratic formula from the variant
41:07 - Conclusion (key takeaways)
43:21 - Fun with joke poll questions

[hLofA]

"We all forget a variable here or there"
He's like the arithmetic Bob Ross

[nestoreleuteriopaivabendo]

Grant, I use the quadratic formula just everyday. It's built in my spreadsheets for computing the steel area needed for reinforced concrete beams.

The same thing we (Structural Engineers) use for calculating reinforced concrete slabs.

For columns, the coefficients change and the forces applied harden the problem, and the result isn't a parabola, but a revolution elipsoid (yes, I know, fellows, that the exact shape is uncertain and is not an exact elipsoid, but think not of the full problem, with second order effects, but of the basic problem, just first order effect).

Quadratic formula is my everyday breakfast, lunch and dinner. Is my drink. I breath it. I bath on it.

And yet you have something to teach me!

Thanks for the update, Grant. Thanks for all you do.

[eskilwadsholt]

m ± √(m² - p) is such a meaningful way to put it. Leibniz stressed the importance of choosing meaningful symbols to serve as a vehicle for thought. That is exactly what that is! All that a, b, c, D stuff brings no mental image to my mind, which is now officially blown. Having taught maths for so long, even using that factoring trick, but the dots were still not connected until now. Thank you!

[Chiramisudo]

You're ability to make complex mathematical topics easy to understand with excellent visuals is astonishing. I think I speak for the entire Internet when I say how profoundly grateful we are that you're not just some stuffy professor in a university where only a small handful of students get the privilege of learning from you. Instead, you generously share your talents with the world and we have all become your students. I'm tremendously grateful for your videos Grant and they have caused me to fall in love with math again! Also, it's nice to finally see your face.

[thasyashetty]

I still can't get over your explanation for the second most popular integer chosen as 69. That is why i love this channel!

[pranavmoghe]

47:39
Yup, totally that's exactly the reason.
You are right Grant.

[NXaiUL]

Grant every bit the maths teacher I ever wished for. Dream come true.

[thelunes]

As a 27 year old grad student, I am not the intended audience for this, but I'd be lying if I said I hadn't been looking forward to the lecture.

[ili]

I love this dude. He's a consummate teacher and an inspiration to us other teachers

[veerzara]

Great ideas from a great teacher:
- The best way to expand your understanding about any subject is when you connect it with real life problems.
- Try to see the concept by different visions since that lets it sink deep in your mind. As an example: look to the quadratic formula using geometry by changing the variable X by a rectangular and the rest by the suitibale geometrical shapes.
- The ultimate way to learn is to practice what you learn immediately.
- Do not stop if you find yourself go out of the topic. Math likes making connections.
- To go from A to C, look for another point B which will decrease the difficulty.

[JasperRLZ]

Fun fact, there's a re-arrangement of terms of the quadratic formula, known in computer graphics circles as "citardauq" ("quadratic" spelled backwards), which provides better precision on computers with floating-point numbers. Whenever you draw a Bezier curve with the pen tool in Photoshop, root-finding is one of the approaches we use to draw it, and the "citardauq" formula is what's used there.

[closmasmas]

That geometric representation of the difference of squares was so satisfying

[Citius]

Grant, I had asked my 14-yr old son to watch this live yesterday (he loved it!), and I came back to enjoy it myself today...truly wonderful. Thank you! So great to see you adding such mathematical beauty into this world, and sharing it with all of us. Your channel is a favorite of mine, and now even more so. By the way, my number would have been 137 for the fine structure constant. Please keep doing these. I will contribute to your Patreon in my appreciation for what you add to this world

[XoIoRouge]

In class with normal teacher: If a negative is in a square root, then we'll just say the roots don't exist. Don't worry about it.

3b1b: **Keeps going**

[deleenstallings]

It’s been bugging me for a while as a math teacher that the formula for finding the x-coordinate of the vertex and the descriminant are taught separately and then students are taught the quadratic formula as though they are separate ideas.

The quadratic formula is this beautiful combination of the two that you explain in a unique way, here.

I love how this explanation focuses on that idea by making “m” your “-b/2a” (in a slightly different order). Then you attach meaning to how the desriminant finishes finding your solutions, or zeros. Conceptually this is beautiful on several levels.

[.]

That's definitely why 69 is such a popular number