Methods to find solutions
Methods to Solve Quadratic Equations
Below are the four most commonly used methods to solve quadratic equations. Click on any link to learn more about any of the methods.
- The Quadratic Formula (Quadratic formula in depth)
- Factoring (Factoring Method in depth)
- Completing the Square
- Factor by Grouping
A quadratic equation is an equation that can be written as ax ² + bx + c where a ≠ 0
In other words, a quadratic equation must have a squared term as its highest power.
Examples of quadratic equations
- y = 2x² + 3x + 5
- y = 13x² + 22
- y = x² − 4x +5
- y = −x² + 5
Examples of equations that are NOT quadratic
- y = 11x + 22
- y = x3 − 4x² + 5x + 6
- y = 2x3 − 7x²
- y = −x4 + 5
The solution of a quadratic equation is the value of x when you set the equation equal to zero
Graphically, since a quadratic equation represents a parabola. The solution (for real numbers) is where the parabola cross the x-axis.
When you solve the following general equation: 0 = ax² + bx + c
Given a quadratic equation: ax ² + bx + c
The quadratic formula is: