Solve a Quadratic Equation

Methods to find solutions

Picture of a quadratic equation

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.

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.

i.e.

When you solve the following general equation: 0 = ax² + bx + c

Given a quadratic equation: ax ² + bx + c

The quadratic formula below will solve the equation for zero

The quadratic formula is: Picture of the quadratic formula