DACC Spring 2025 CCDM 114 - Quadratic Formula Concepts

These flashcards cover key vocabulary and concepts related to the quadratic formula and its application in solving quadratic equations.

Quadratic Formula

A formula used to solve quadratic equations in the form of ax² + bx + c = 0, expressed as X = (-b ± √(b² - 4ac)) / (2a).

Discriminant (D)

The part of the quadratic formula under the square root, defined as D = b² - 4ac; it determines the nature of the roots.

Real solutions

Conditions under which the solutions of a quadratic equation are real numbers; occurs when the discriminant is positive (D > 0).

Repeated solutions

Occurs when the discriminant is zero (D = 0), leading to one real repeated root.

No real solutions

Occurs when the discriminant is negative (D < 0), resulting in complex roots.

Coefficient (a, b, c)

In a quadratic equation of the form ax² + bx + c = 0, 'a' is the coefficient of x², 'b' is the coefficient of x, and 'c' is the constant term.

Standard Form of Quadratic Equation

The standard form of a quadratic equation is written as ax² + bx + c = 0.

Factoring

A method for solving quadratic equations by expressing them as a product of their linear factors.