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.
Notes: Step 0: Solve Quadratic Formula using the PQ Substitution Method
Written notes — mirrored from Cubic Formula Proof, which walks through the complete derivation.
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- Full written notes: Cubic Formula Proof
- Playlist: Cubic Formula Proof YouTube playlist
- More math: mes.fm/math
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