Quadratic Equations — Formula Sheet

ax^2+bx+c=0, a≠0

D=b^2-4ac

x=(-b±√(b^2-4ac))/(2a)

V(-b/(2a),-D/(4a))

D>0 → real and distinct roots

D=0 → real and equal roots

D<0 → complex and distinct roots

α=(-b+√D)/(2a), β=(-b-√D)/(2a)

y=ax^2+bx+c

If a>0, y_min=-D/(4a) at x=-b/(2a)

If a<0, y_max=-D/(4a) at x=-b/(2a)

α+β=-b/a

αβ=c/a

x^2-(sum of roots)x+(product of roots)=0

1/α+1/β=(α+β)/(αβ)

α^2+β^2=(α+β)^2-2αβ

A quadratic equation has the form ax^2 + bx + c = 0, where a does not equal 0.

The discriminant is D = b^2 - 4ac.

The graph of y = ax^2 + bx + c is a parabola.

If alpha and beta are roots of ax^2 + bx + c = 0, then alpha + beta = -b/a.

If alpha and beta are roots of ax^2 + bx + c = 0, then alpha beta = c/a.

Quadratic equation

ax^2 + bx + c = 0, a != 0

Quadratic formula

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

The discriminant is D = b^2-4ac.