Solving Quadratic Equations and Inequalities

Solving Quadratic Equations

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 xx-axis is the number of real solutions.
  • A graph may only give approximate values of the xx-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.