3.7: Solving Quadratic Equations by the Quadratic Formula

Objectives Learn the Quadratic Formula Use the QF to determine the number of solutions to a quadratic function Use the QF to find the solutions to a quadratic function

Concept: The Quadratic Formula When a quadratic that is written in Standard Form , won’t factor apart nicely, we can still find the roots by using the: Quadratic Formula: The Quadratic Formula will let you solve ANY quadratic equation.

Concept: The Discriminant: The discriminant is the piece of the quadratic formula that is under the radical: b2 – 4ac

Concept: The Discriminant cont… 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.

Concept: The Discriminant cont… Value of the Discriminant Nature of the Solutions Negative 2 imaginary solutions Zero 1 Real Solution Positive – perfect square 2 Reals- Rational Positive – non-perfect square 2 Reals- Irrational

Concept: The Discriminant cont… 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) a=2, b=7, c=-11 Discriminant = Value of discriminant=137 Positive-NON perfect square Nature of the Roots – 2 Reals - Irrational Discriminant =

Concept: The Discriminant cont… Example #1 continued Solve using the Quadratic Formula

Concept: You Try!!! Try the following examples. Do your work on your paper and then check your answers.