Andrew's git - notes.git/blob - methods/functions.md

   1# Linear and Quadratic Functions
   2
   3## General binomial expansion
   4
   5$$(a+b)(c+d) = a(c+d) + b(c+d)$$
   6$$= ac+ad+bc+bd$$
   7
   8## Perfect square expansion
   9
  10$$(a+b)^2=a^2+2ab+b^2$$
  11
  12## Difference of perfect squares
  13
  14$$ a^2-b^2=(a+b)(a-b)$$
  15
  16## Factorising monic quadratics
  17
  18$$x^2+bx+c = (x+e)(x-f)$$
  19
  20where
  21$e \times f = c$
  22$e+f = b$
  23
  24## Factorising general quadratics
  25
  26$ax^2+bx+c=(x+e)(x+f)$
  27
  28where
  29$e \times f = a \times c$
  30$e+f = b$
  31
  32## Completing the square
  33
  34$ax^2+bx+c=a(x + (b \over 2a))^2+(c-{b^2 \over 2a})^2$
  35
  36## Axis of symmetry
  37
  38${vert}_x={-b \over 2a}$
  39
  40$x={-b \over 2a}$
  41(corresponding line)