Formula Sheet

Formula	Expression
Roots	x = (-b ± sqrt(D))/(2a)
Discriminant	D = $b^2$ - 4ac
Sum of roots	-b/a
Product of roots	c/a
Difference of roots	sqrt(D)/\|a\|
$alpha^2$ + $beta^2$	(alpha+beta)^2 - 2alphabeta
$alpha^3$ + $beta^3$	(alpha+beta)^3 - 3alphabeta*(alpha+beta)
1/alpha + 1/beta	-b/c
alpha* $beta^2$ + $alpha^2$ *beta	alphabeta(alpha+beta) = -bc/ $a^2$
Vertex x-coordinate	- $\frac{b}{2a}$
Vertex y-coordinate	- $\frac{D}{4a}$
Min/Max value of f(x)	- $\frac{D}{4a}$ (min if a>0, max if a<0)
Common root condition	(c1a2-c2a1)^2 = (a1b2-a2b1)(b1c2-b2c1)