Quadratic formula

Math

Definition

A formula that gives the solutions to any quadratic equation ax² + bx + c = 0. It works for all quadratic equations, including those that cannot be factored easily.

Examples

  • For x² - 5x + 6 = 0: x = (5 ± √1)/2, giving x = 3 or x = 2
  • For x² + x + 1 = 0: discriminant is negative, so no real solutions
  • Finding when a projectile hits the ground from h = -16t² + 48t + 5
Key Fact

x = (-b ± √(b² - 4ac)) / (2a)

Related Terms

Discriminant Completing the square Solving by factoring Vertex form

Study This Concept

Practice quadratic formula with free review games in these units:

Algebra 1 Unit 8: Quadratic Equations