Math Tutorial 9.6 - The Quadratic Formula

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There are 4 lessons in this math tutorial covering The Quadratic Formula. The tutorial starts with an introduction to The Quadratic Formula and is then followed with a list of the separate lessons, the tutorial is designed to be read in order but you can skip to a specific lesson or return to recover a specific math lesson as required to build your math knowledge of The Quadratic Formula. you can access all the lessons from this tutorial below.

In this Math tutorial, you will learn:

  • What is a quadratic formula? What is it used for?
  • What is the discriminant? What does it tell about a quadratic equation?
  • What are some applications of quadratic equations in practice?
  • What are Vieta's Formulas? Why do we use them?
  • How do Vieta's Formulas help us find the original coefficients of a quadratic equation?


In the previous tutorial, we dealt extensively with quadratic equations. What methods did you learn in that tutorial? Can you solve all quadratic equations using the methods explained in it?

Try to solve this quadratic equation:

3x2 - 2x + 1 = 0

Can you solve it? Why?

Some quadratic equations are very challenging to solve by using the factorization methods or by completing the square. Moreover, some other quadratic equations may have decimal or even real roots, so it is very difficult to find a suitable factorization for them. Other quadratic equations (such as the one shown above) may not have any real root at all. One may try unsuccessfully from morning to evening to solve such equations by factorization or by completing the square, without even realizing that such an equation has no solution. Therefore, it becomes necessary to use a more comprehensive and inclusive method for solving quadratic equations or at least to become aware of quadratic equations that have no solutions. This method consists of the use of the quadratic formula, which we are going to explain in this tutorial.

Please select a specific "The Quadratic Formula" lesson from the table below, review the video tutorial, print the revision notes or use the practice question to improve your knowledge of this math topic.

Equations Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
9.6The Quadratic Formula
Lesson IDMath Lesson TitleLessonVideo
9.6.1Quadratic Formula Definition
9.6.2The Meaning of Discriminant
9.6.3Quadratic Equations in Practice
9.6.4Vieta's Formulas

Whats next?

Enjoy the "The Quadratic Formula" math tutorial? People who liked the "The Quadratic Formula" tutorial found the following resources useful:

  1. Math tutorial Feedback. Helps other - Leave a rating for this tutorial (see below)
  2. Equations Video tutorial: The Quadratic Formula. Watch or listen to the The Quadratic Formula video tutorial, a useful way to help you revise when travelling to and from school/college
  3. Equations Revision Notes: The Quadratic Formula. Print the notes so you can revise the key points covered in the math tutorial for The Quadratic Formula
  4. Equations Practice Questions: The Quadratic Formula. Test and improve your knowledge of The Quadratic Formula with example questins and answers
  5. Check your calculations for Equations questions with our excellent Equations calculators which contain full equations and calculations clearly displayed line by line. See the Equations Calculators by iCalculator™ below.
  6. Continuing learning equations - read our next math tutorial: Systems of Linear Equations. Methods for Solving Them.

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