More than one method may be appropriate for solving a quadratic equation based on the characteristics of the equation.
More than one method is possible to solve quadratic equations. The method chosen for a particular equation may depend on factorability and personal preference.
Graphing: Use with technology or when approximate values give enough information about the solutions.
- Graphing the related quadratic function can quickly show the number of solutions.
- The number of times that the graph touches or crosses the -axis is the number of real solutions.
- A graph may only give approximate values of the -intercepts, so another method may be necessary to find exact solutions.
Factoring: Use when a quadratic expression is easily factorable.
- Factoring methods may include looking for a pattern such as a difference of squares or a perfect square trinomial.
- Factoring gives exact solutions.
Completing the square: Use when a quadratic expression is not factorable.
- Completing the square works for all quadratic equations, even when the quadratic expression is not factorable.
- Completing the square gives exact solutions.
Quadratic formula: Use with any quadratic equation.
- The quadratic formula works for all quadratic equations, even when the quadratic expression is not factorable.
- The quadratic formula gives exact solutions.
- The discriminant tells how many real solutions the equation has.