The videos for the derivation of the quadratic formula are of varying quality but most of them are in the tradition of well-organized exposition and highly procedural. While I can understand the impulse showing students how the Formula was invented and thereby providing a concrete example of the usefulness of abstract symbolic manipulation the computations involved are often a bit beyond the average student at this point. Thanks to all of you who support me on Patreon.
This video is a derivationproof of the quadratic formula by using completing the square.
The process we were taught was to find two numbers such that they add up to b and multiplication equals ac. The internet has many resources -- lesson plans videos and presentations. First we bring the equation to the form ax²bxc0 where a b and c are coefficients. Complete the square by adding b2 4 a2 to both sides of the equation.