Quadratic Formula by the PQ Substitution Method

In this video I solve the quadratic formula again, but this time using the PQ method instead of the complete the squares method that I used earlier. This is because the PQ method is utilized throughout the cubic formula proof, so this is a good preview. The procedure starts off the same as before, by dividing out the quadratic equation by a, but now we set p = b/a and q = c/a. We can now shift the parabola, which is just a quadratic equation, by setting x = y + k in order to cancel out the px term. Expanding out, we find that the value k = -p/2 cancels out the px term, thus allowing us to solve for y. Plugging y back into x, we obtain the PQ version of the quadratic formula.

Time stamps

• Solve quadratic formula using PQ substitution: 0:00
• Set p = b/a and q = c/a to get PQ version of quadratic equation: 0:40
• Shift parabola to remove px term by setting x = y + k: 1:02
• Set k = -p/2 to cancel out px terms: 2:33
• Rearrange to solve for y: 5:13
• Plug y back into x to obtain PQ formula: 5:37
• PQ formula: 6:30

Notes and playlists

• Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EF05ExjzLbB64NgUjoV1hl
• Notes: @mes/dzekfnxh .

Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

MES Links: https://mes.fm/links

MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: @mes

Email me: [email protected]

Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps

▶️ 3Speak