Question

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

Answer 1

The standard form of a quadratic equation is:

`ax^2+bx+c=0`,
`a\\eq 0`

Quadratic Formula Derivation:

`ax^2+bx+c=0\\`

`$x^2+(b)/(a)x+(c)/(a) =0 $`

`$x^2+(b)/(a)x = -(c)/(a)$`

Completing the Square:

`$x^2+(b)/(a)x +(b^2)/(4a^2) = (b^2)/(4a^2)-(c)/(a)$`

`$ ( x+(b)/(2a) )^2 = (b^2-4ac)/(4a^2) $`

Square Root property:

`$x+(b)/(2a) = \pm \sqrt{ (b^2-4ac)/(4a^2)} $`

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

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