Solving Quadratic Equations

Vocabulary flashcards for key concepts and methods related to solving quadratic equations.

Quadratic Formula

A formula used to find the solutions (roots) of a quadratic equation in the form ax² + bx + c = 0; x = (-b ± √(b²-4ac)) / (2a)

Discriminant

The value under the square root in the quadratic formula (b²-4ac) which determines the nature and number of solutions of the quadratic equation.

Completing the Square

A method of solving quadratic equations by manipulating the equation to create a perfect square trinomial on one side.

Factoring

A method of solving quadratic equations by expressing the quadratic expression as the product of two linear factors.

Discriminant Interpretation (Δ > 0)

If Δ > 0, the quadratic equation has two distinct real solutions.

Discriminant Interpretation (Δ = 0)

If Δ = 0, the quadratic equation has exactly one real solution (a repeated root).

Discriminant Interpretation (Δ < 0)

If Δ < 0, the quadratic equation has no real solutions, but two complex solutions.