Quadratic Systems

Completing the Square

Rewriting a quadratic to reveal its vertex — and solve it.

Factoring — GCF and Difference of Squares

Pull out what every term shares, then look for the pattern that splits a square into two.

Factoring Trinomials

Breaking a quadratic expression into two binomials you can multiply back together.

Operations with Radicals

How to add, subtract, multiply, and divide square roots.

Quadratic and Linear Systems

How a line and a parabola can meet — and what it means when they don't.

Simplifying Radicals

Breaking square roots down to their simplest form.

Solving Quadratics by Factoring

Split a quadratic into two factors, then use the fact that a product of zero means at least one factor is zero.

Solving Quadratics by Taking Square Roots

When a quadratic has no x term, you don't need to factor — just undo the square.

The Discriminant and Nature of Roots

One expression tells you everything about a quadratic's solutions before you solve it.

The Quadratic Formula

A single formula that solves every quadratic equation.