The Quadratic Formula Students will be able to

The Quadratic Formula Students will be able to solve quadratic equations by using the quadratic formula. FHS Quadratic Function

Solving Quadratic Equations • You have learned several methods for solving quadratic equations: graphing, factoring, using square roots, and completing the square. • Another method is to use the Quadratic Formula, which allows you to solve a quadratic equation in standard form. • Make sure that the equation is in standard form before you use the quadratic formula. FHS Quadratic Function 2

The Quadratic Formula • If ax 2 + bx + c = 0 and a ≠ 0, then the solutions of the equation are: • You can use the Quadratic Formula to solve any quadratic equation that is written in standard form. FHS Quadratic Function 3

The Discriminant • The discriminant is part of the Quadratic Formula that is under the radical sign. Discriminant • If the discriminant is equal to zero, then there is only one real solution for the quadratic equation. • If it is positive, there are two real solutions. • If it is negative, there are two complex solutions. FHS Quadratic Function 4

Example: • Use the quadratic formula to solve the following equation: • First change equation to standard form: where a = 2, b = – 1, c = – 3 • Then use the quadratic formula: FHS Quadratic Function 5