How was the Quadratic Formula Derived?

Note:

Ever wonder how mathematicians came up with the quadratic formula? Wonder no more! This tutorial takes you through the process of deriving the quadratic formula, so even if you forget it on an exam, you'll be able to derive it and then use it to solve your quadratic equation! Check it out!

Keywords:

quadratic formula
derivation
proof
equation
completing the square

Background Tutorials

Fraction Basics
- What's a Numerator and What's A Denominator?
  
  Numerators and denominators are the key ingredients that make fractions, so if you want to work with fractions, you have to know what numerators and denominators are. Lucky for you, this tutorial will teach you some great tricks for remembering what numerators and denominators are all about.
Adding Real Numbers
- How Do You Find a Common Denominator and a Least Common Denominator?
  
  This tutorial gives you some practice finding a common denominator and the least common denominator of three fractions. There's only one least common denominator, but there are many common denominators. This tutorial gives you one. Can you find another?
Subtracting Real Numbers
- How Do You Subtract Fractions with the Same Denominator?
  
  Subtracting fractions with like denominators? Just subtract the numerators and put the result over the common denominator! To see this process in action, check out this tutorial!
Dividing Real Numbers
- What's the Reciprocal Rule of Division?
  
  When you divide fractions, the trick is to rewrite division as a multiplication. But the truth is that you can always rewrite division as a multiplication, and in this tutorial you'll see the rule that makes that possible!
Simplifying Expressions
- What's a Coefficient?
  
  There is a bunch of vocabulary that you just need to know when it comes to algebra, and coefficient is one of the key words that you have to feel 100% comfortable with. Check out the tutorial and let us know if you want to learn more about coefficients!
Properties of Equality
- What's the Subtraction Property of Equality?
  
  Solving equations can be tough, especially if you've forgotten or have trouble understanding the tools at your disposal. One of those tools is the subtraction property of equality, and it lets you subtract the same number from both sides of an equation. Watch the video to see it in action!
- What's the Addition Property of Equality?
  
  Solving equations can be tough, especially if you've forgotten or have trouble understanding the tools at your disposal. One of those tools is the addition property of equality, and it lets you add the same number to both sides of an equation. Watch the video to see it in action!
Factoring Perfect Square Trinomials
- How Do You Use a Shortcut to Factor a Perfect Square Trinomial?
  
  Factoring a perfect square trinomial? Did you know there's a shortcut to factoring this special kind of trinomial? Check it out! It's pretty cool, and it may make this process a little faster!
Graphing Definitions and Examples
- What is a Quadratic Equation?
  
  You can't go through algebra without seeing quadratic equations. The graphs of quadratic equations are parabolas; they tend to look like a smile or a frown. There's also a bunch of ways to solve these equations! Watch this tutorial and get introduced to quadratic equations!
Solving Quadratics by Completing the Square
- How Do You Solve a Quadratic Equation by Completing the Square?
  
  One of the many ways you can solve a quadratic equation is by completing the square. In this method, you want to turn one side of the equation into a perfect square trinomial. This tutorial takes you through the steps of solving a quadratic equation by completing the square. Check it out!
Solving Quadratics Using the Quadratic Formula
- What is the Quadratic Formula?
  
  If you're solving quadratic equations, knowing the quadratic formula is a MUST! This formula is normally used when no other methods for solving quadratics can be reasonably used. In this tutorial, learn about the quadratic formula and see it used to solve a quadratic equation. Take a look!