Our subscribers' gradelevel estimate for this page: 5th  6th 
More Math Activities 
EnchantedLearning.com Algebra: Quadratic Equations 
Quadratic Equation: 
A quadratic equation can be written in the form:
,
where a, b, and c are numbers (a ≠0), and x is the variable. x is a solution (or a root) if it satisfies the equation
Some examples of quadratic equations include:


Most seconddegree equations are more difficult to solve, and cannot be solved by simple factoring. The quadratic formula is a general way of solving any quadratic equation:
This formula gives two solutions, although the two solutions may be the same number. (When solving any polynomial equation of degree n, there are at most n solutions to that equation.)
Divide each side of the equation by a.
Subtract c/a from each side of the equation.
Add (b/2a)^{2} to each side of the equation (to complete the square).
Find a common denominator for the right side of the equation.
Take the square root of each side of the equation.
Add b/2a to each side of the equation.
The plusorminus sign shows that there are two possible solutions.

Every quadratic equation has at most two solutions, but for some equations, the two solutions are the same number, and for others, there is no solution on the number line (because it would involve the square root of a negative number).
One way to understand this visually is to realize that when you graph a quadratic equation (a seconddegree equation), you get a parabola. When you set the quadratic equation equal to zero, this represents the points where the parabola hits the xaxis (the xintercepts, where y=0).
Quadratic Equations Worksheets (with no linear term) Solve simple (pure) quadratic equations (no linear terms). 
Enchanted Learning^{®}
Over 35,000 Web Pages
Sample Pages for Prospective Subscribers, or click below
Overview of Site What's New Enchanted Learning Home Monthly Activity Calendar Books to Print Site Index K3 Crafts K3 Themes Little Explorers Picture dictionary PreK/K Activities Rebus Rhymes Stories Writing Cloze Activities Essay Topics Newspaper Writing Activities Parts of Speech Fiction The Test of Time iPhone app TapQuiz Maps  free iPhone Geography Game

Biology Animal Printouts Biology Label Printouts Biomes Birds Butterflies Dinosaurs Food Chain Human Anatomy Mammals Plants Rainforests Sharks Whales Physical Sciences: K12 Astronomy The Earth Geology Hurricanes Landforms Oceans Tsunami Volcano 
Languages Dutch French German Italian Japanese (Romaji) Portuguese Spanish Swedish Geography/History Explorers Flags Geography Inventors US History Other Topics Art and Artists Calendars College Finder Crafts Graphic Organizers Label Me! Printouts Math Music Word Wheels 
Click to read our Privacy Policy
Search the Enchanted Learning website for: 
Copyright ©20052016 EnchantedLearning.com  How to cite a web page