Solving Quadratic Equations by the Quadratic Formula Section 4.8

THE QUADRATIC FORMULA 1.When you solve using completing the square on the general formula you get: 2.This is the quadratic formula! 3.Just identify a, b, and c then substitute into the formula.

WHY USE THE QUADRATIC FORMULA? The quadratic formula allows you to solve ANY quadratic equation, even if you cannot factor it. An important piece of the quadratic formula is what’s under the radical: b 2 – 4ac This piece is called the discriminant.

WHY IS THE DISCRIMINANT IMPORTANT? The discriminant tells you the number and types of answers (roots) you will get. The discriminant can be +, –, or 0 which actually tells you a lot! Since the discriminant is under a radical, think about what it means if you have a positive or negative number or 0 under the radical.

WHAT THE DISCRIMINANT TELLS YOU! Value of the DiscriminantNature of the Solutions Negative2 imaginary solutions Zero1 Real Solution Positive – perfect square2 Reals- Rational Positive – non-perfect square 2 Reals- Irrational

Example #1 Find the value of the discriminant and describe the nature of the roots (real,imaginary, rational, irrational) of each quadratic equation. Then solve the equation using the quadratic formula) 1. a=2, b=7, c=-11 Discriminant = Value of discriminant=137 Positive-NON perfect square Nature of the Roots – 2 Reals - Irrational

Example #1- continued Solve using the Quadratic Formula

Solving Quadratic Equations by the Quadratic Formula Try the following examples. A)Find the discriminant and describe the nature of the roots. B) Solve using the quadratic formula.