Understanding Quadratic Equations

Front

Standard form of a quadratic equation

Back

ax^2 + bx + c = 0

Front

Quadratic formula

Back

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Front

Discriminant of a quadratic equation

Back

b^2 - 4ac

Front

Nature of roots when discriminant > 0

Back

Two distinct real roots

Front

Nature of roots when discriminant = 0

Back

One real root (repeated)

Front

Nature of roots when discriminant < 0

Back

No real roots (complex roots)

Front

Example: Solve x^2 - 5x + 6 = 0

Back

x = 2, x = 3

Front

Example: Solve x^2 + 4x + 4 = 0

Back

x = -2 (repeated root)

Front

Example: Solve x^2 + x + 1 = 0

Back

No real roots (complex roots)

Front

Vertex form of a quadratic equation

Back

y = a(x-h)^2 + k