Linear and Quadratic Functions

General binomial expansion

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

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

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

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

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

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

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

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

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

(corresponding line)