A non-associative algebra $A$ (with unity $1_A$ over a commutative ring $R$ (with unity $1_R$ is called a quadratic algebra if $A$ admits a quadratic form $Q\colon A\to R$ such that

1. $Q(1_A)=1_R$
2. the quadratic equation $x^2-b(1_A,x)x+Q(x)1_A=0$ is satisfied by all $x\in A$ where $b$ is the associated symmetric bilinear form given by $b(x,y):=Q(x+y)-Q(x)-Q(y)$