Question

Descried how to derive the quadratic formula from a quadratic equation in standard form

Answer 1

Answer:

The standard form of a quadratic equation is:

$ax^2+bx+c=0$, $a\neq 0$

Quadratic Formula Derivation:

$ax^2+bx+c=0$

$x^2+\frac{b}{a}x+\frac{c}{a} =0$

$x^2+\frac{b}{a}x = -\frac{c}{a}$

Completing the Square:

$x^2+\frac{b}{a}x +\frac{b^2}{4a^2} = \frac{b^2}{4a^2}-\frac{c}{a}$

$( x+\frac{b}{2a} )^2 = \frac{b^2-4ac}{4a^2}$

Square Root property:

$x+\frac{b}{2a} = \pm \sqrt{ \frac{b^2-4ac}{4a^2}}$

$x = -\frac{b}{2a} \pm { \frac{\sqrt {b^2-4ac}}{2a}}$

$x = \frac{-b\pm\sqrt{b^2-4ac}} {2a} }$