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Solving Quadratic Equations




 
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More Lessons for Basic Algebra

Math Worksheets

A series of free, online Basic Algebra Lessons.

In tis lesson, we will learn

  • vocabulary of quadratic polynomials
  • how to solve quadratic equations by factoring
  • how to solve quadratic equations using square roots
  • how to solve quadratic equations by completing the square


Vocabulary of Quadratic Polynomials

Polynomials Quadratic equations and functions have a lot of complex vocabulary that can make them difficult to solve. When solving quadratic polynomials, there are several different ways to instruct students on how to find the roots, find the solutions, find the x-intercepts or find the zeroes of polynomial functions and quadratic graphs.
How to label the roots of a quadratic polynomial, solutions to a quadratic equation, and x-intercepts or roots of a quadratic function.
Short definitions for Parabola, axis of symmetry, vertex, maximum, minimum, solutions and the discriminant.

Solving Quadratic Equations by Factoring

When we solve quadratic equations, we have several different methods that we can choose from. Solving quadratic equations by factoring is just one of those methods. When solving quadratic equations by factoring, we set one side of the equation to zero and then factor the quadratic equation so that we can use the zero product property to determine where x = 0. Quadratic equations can also be solved by using square roots, completing the square or the quadratic formula.

Solving Quadratic Equations by Factoring - Basic Examples



Solving Quadratic Equations by Factoring - Another Example

Solving Quadratic Equations using Square Roots

Solving quadratics can be difficult and solving quadratics using square roots is just one of the methods of solving a quadratic equation. Solving a quadratic equation using square roots works best when we have a quadratic equation that does not have a "b" term and by taking the square root of either side of the equation. Quadratic equations can also be solved by factoring, completing the square or the quadratic formula.

This video explains how use square roots to solve quadratic equations in the form ax2 + c = 0.


 
This video provides examples on how square roots can be used to solve certain types of quadratic equations

Completing the Square

Completing the square is one method for solving a quadratic equation. A quadratic equation can also be solved by several methods including factoring, graphing, using the square roots or the quadratic formula. Completing the square will always work when solving quadratic equations and is a good tool to have. Solving a quadratic equation by completing the square is used in a lot of word problems.

Completing the Square - Solving Quadratic Equations.
This video shows an easier example of completing the square.


Completing the Square - Solving Quadratic Equations.
This video shows a slightly harder example of completing the square to solve a quadratic equation.



Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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