Investigation: Derive the Quadratic Formula (HSC SSCE Mathematics Advanced): Flashcards

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

$ax^2 + bx + c = 0$

Completing the square

$b^2 - 4ac$

Two solutions (or one repeated solution)

Can be negative

Divide every term by $a$

$\left(\frac{b}{2a}\right)^2 = \frac{b^2}{4a^2}$

$x = 2$ or $x = -4$

Nature of the solutions