# Linear and Quadratic Functions

## General binomial expansion

$$(a+b)(c+d) = a(c+d) + b(c+d)$$
$$= ac+ad+bc+bd$$

## Perfect square expansion

$$(a+b)^2=a^2+2ab+b^2$$

## Difference of perfect squares

$$ a^2-b^2=(a+b)(a-b)$$

## Factorising monic quadratics

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

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)