Quadratic Formula
Gives roots of any quadratic.
Key idea
Gives roots of any quadratic.
In depth
For ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) / (2a). It is the result of completing the square on the general quadratic, so it works every time.
Worked example
2x² − 3x − 2 = 0: x = (3 ± √(9 + 16))/4 = (3 ± 5)/4, so x = 2 or x = −1/2.
Formula
Real-world uses
- Solving any quadratic model for a launch, profit or area problem in engineering and business
Common mistake
Dividing only part of the numerator by 2a.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Quadratic Formula?
Gives roots of any quadratic. It is a topic at the advanced level in Algebra.
What is the formula for Quadratic Formula?
The key formula is x = (−b ± √(b²−4ac)) / 2a.
Where is Quadratic Formula used in real life?
Real-world examples: Solving any quadratic model for a launch, profit or area problem in engineering and business.
What should I learn before Quadratic Formula?
Make sure you are comfortable with Completing the Square, the previous topic in Algebra.
What is a common mistake with Quadratic Formula?
Dividing only part of the numerator by 2a.
How can I practise Quadratic Formula?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Quadratic Formula?
Move on to Discriminant next.
Related advanced topics in Algebra
- Absolute Value Inequalities – Rewrite as a compound inequality.
- Systems with Three Variables – Reduce to two variables then solve in sequence.
- Systems of Inequalities – Solution region is the overlap of half-planes.
- Factoring by Grouping – Group terms in pairs to find a common binomial.
- Sum and Difference of Cubes – Special factoring patterns for cubes.
- Completing the Square – Rewrite a quadratic as a perfect square plus constant.