Another view on the quadratic formula.
Full playlist:    • Lockdown math  
Home page: https://www.3blue1brown.com
Brought to you by you: https://3b1b.co/ldm-thanks

Beautiful pictorial summary by @ThuyNganVu:
  / 1258217451323416577  

Po Shen Loh on quadratics:
   • A Different Way to Solve Quadratic Eq...  

Welch Labs on imaginary numbers:
   • Imaginary Numbers are Real  

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:
https://vincerubinetti.bandcamp.com/a...

Stream the music on Spotify:
https://open.spotify.com/album/1dVyjw...

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.

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

3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe

Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter:   / 3blue1brown  
Reddit:   / 3blue1brown  
Instagram:   / 3blue1brown_animations  
Patreon:   / 3blue1brown  
Facebook:   / 3blue1brown