Quadratic Equations Review

Flashcards covering key concepts related to quadratic equations, solving methods, and properties.

Quadratic Equation

An equation that can be expressed in the standard form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants and $a \neq 0.

Completing the Square

A method of solving quadratic equations by rewriting the equation in the form $(x - p)^2 = q$.

Real Roots

The solutions to a quadratic equation that can be represented as points on the real number line.

Discriminant

In the quadratic formula $b^2 - 4ac$, it determines the nature of the roots of the quadratic equation: real and distinct if positive, real and equal if zero, and complex if negative.

Roots of a Quadratic Equation

Solutions $x$ for $ax^2 + bx + c = 0$, often found using factoring, completing the square, or the quadratic formula.

Factoring

Breaking down a quadratic equation into simpler expressions that can multiply to yield the original equation.

Vertex Form of a Quadratic Function

A form of a quadratic function represented as $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex.

Standard Form of a Quadratic Function

The form $y = ax^2 + bx + c$. This form is useful for identifying the coefficients quickly.