Derive The Quadratic Formula

Let us find out how the famous Quadratic Formula can be created using a bunch of algebra steps. A Quadratic Equation looks like this: While simply knowing the formula is often enough for many, understanding how it's derived (in other words, where it comes from) is another thing entirely.

The formula is derived via "completing the square" that has other applications in math as well, so it is recommended that you be familiar with it. Learn how the 'horrible looking' Quadratic Formula is derived by steps of Completing the Square. That means any quadratic equation of the form a {x^2} + bx + c = 0 can easily be solved by the quadratic formula.

Combine the right side of the equation to get the quadratic formula. See the derivation below. In this post, well walk you through the step-by-step derivation of the quadratic formula using the method of completing the square, and explain why its universally applicable.

Any generic method or algorithm for solving quadratic equations can be applied to an equation with symbolic coefficients and used to derive some closed-form expression equivalent to the quadratic formula. Introduction The solution formula to the quadratic equation ax2 + bx + c = 0 (1) is usually derived in textbooks by completing the square. This is done in the following way (see [1]):

The following diagram shows how to derive the Quadratic Formula. Scroll down the page for more examples and solutions on how to use the quadratic formula to solve equations. This Quadratic Formula Derivation is written in an easy-to-understand step-by-step format with Warm Ups to make important connections.

It provides a systematic approach that can be used to find the roots of any quadratic equation in the form ax^2 + bx + c = 0. In this article, well break down the process into eight steps to help you understand and derive the quadratic formula easily.