Linear and Quadratic Functions

General binomial expansion

Perfect square expansion

Difference of perfect squares

Factorising monic quadratics

where
$e \times f = c$
$e+f = b$

Factorising general quadratics

$ax^2+bx+c=(x+e)(x+f)$

where
$e \times f = a \times c$
$e+f = b$

Completing the square

$ax^2+bx+c=a(x + (b \over 2a))^2+(c-{b^2 \over 2a})^2$

Axis of symmetry

${vert}_x={-b \over 2a}$

$x={-b \over 2a}$
(corresponding line)