Deriving the Quadratic Formula

This page outlines the derivation of the Quadratic Formula.

We take a quadratic equation in its general form, and solve for x:

a⁢x2+b⁢x+c=0a⁢x2+b⁢x=−cx2+ba⁤x=−caDivide out leading coefficient.x2+ba⁤x+(b2a)2=−c(4a)a(4a)+b24a2Complete the square.(x+b2a)(x+b2a)=b2−4ac4a2Discriminant revealed.(x+b2a)2=b2−4ac4a2x+b2a=b2−4ac4a2x=−b2a±{C}b2−4ac4a2There's the vertex formula.x=−b±{C}b2−4ac2aTODO