Equations

Quadratic equation

Keywords:

ax2+bx+c=0

Solutions of a quadratic equation

x1,2=-b±b2-4ac2a

Factors of a a quadratic equation:

ax2+bx+c=ax-x1x-x2

Vieta's formulas:

x1+x2=-ba  ;  x1·x2=ca

Discriminant:

D=b2-4ac
D>0 x1 , x2   two different real solutions
D=0 x1=x2   one real solution
D<0 x1=x2¯   no real solution (two complex conjugate solutions)

Quadratic equation as a function

y=ax2+bx+c
Graph of a quadratic function

Coordinates of P, vertex of the parabola:

P-b2a,-b2-4aca