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: https://twitter.com/ThuyNganVu/status/1258217451323416577 Po Shen Loh on quadratics: https://www.youtube.com/watch?v=ZBalWWHYFQc 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/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u 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: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown