Quadratic equations & functions

This course is a part of Algebra (all content), a 20-course Topic series from Khan Academy.

This topic covers: - Solving quadratic equations - Graphing quadratic functions - Features of quadratic functions - Quadratic equations/functions word problems - Systems of quadratic equations - Quadratic inequalities

This course contains 12 segments:

Parabolas intro

Learn what parabolas are and about their main features: their general shape, vertex, and axis of symmetry.

Quadratic factored form

The factored form of a quadratic function is an expression that is, well, factored! Like f(x)=(2x+1)(x-3). Learn how to analyze functions given in this form to find their zeros, their vertex, and their graph.

Solving quadratics by taking square roots

In this tutorial you will learn about the most basic way of solving quadratic equations.

Quadratic vertex form

The vertex form of a quadratic function shows the coordinates of the parabola's vertex. For example, the vertex of g(x)=(x-1)²+2 is at (1,2). Learn how to analyze functions given in this form to find their zeros, their vertex, and their graph.

Solving quadratics by factoring

In this tutorial, you'll learn some pretty elaborate ways of solving quadratic equations, by harnessing the mighty strength of algebra.

Completing the square

You're already familiar with factoring quadratics, but have begun to realize that it only is useful in certain cases. Well, this tutorial will introduce you to something far more powerful and general. Even better, it is the bridge to understanding and proving the famous quadratic formula.

The quadratic formula

Learn how to solve any quadratic equation with the most general tool of all, the quadratic formula!

Quadratic standard form

In this tutorial, we will learn how to graph quadratic functions given in different forms.

Features & forms of quadratic functions

Learn about the features of quadratic functions, and how to find them given the formula of the function. Also learn about the different forms of quadratic functions: standard, vertex, and factored.

Transforming parabolas

Learn how function transformations affect the graphs of quadratic functions.

Systems of quadratic equations

Learn how to solve systems of two equations in two variables, where at least one of the equations is quadratic.

Quadratic inequalities

Learn how to solve inequalities that contain quadratic expressions. For instance, solve x^2+3x+2>0.