Solve each equation by factoring. 3x 2 =5x x= {0, 5/3} Homework Quiz

AAT-A Date: 2/10/14 SWBAT complete the square to solve factoring problems  Do Now: Turn in Enrichment Sum of Roots (15 minutes)  HW Requests: pg 318 #15-27 odds pg 303 #42-49; Pg 310 #15-37 odds HW: Worksheets for homework Skills Practice pg 340 Bring Calculators tomorrow or Loan Request  Announcements: Bring Graphing Calculators Complete presentations Life Is Just A Minute Life is just a minute—only sixty seconds in it. Forced upon you—can't refuse it. Didn't seek it—didn't choose it. But it's up to you to use it. You must suffer if you lose it. Give an account if you abuse it. Just a tiny, little minute, But eternity is in it! By Dr. Benjamin Elijah Mays, Past President of Morehouse College

Solving Quadratic Equations by the Quadratic Formula

When to use the Quadratic Formula Use the quadratic formula when you can’t factor to solve a quadratic equation. (or when you’re stuck on how to factor the equation.)

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 Discriminant Nature of the Solutions Example of Graph of Related Function Positive – perfect square 2 Reals- Rational Positive – non- perfect square 2 Reals- Irrational Negative2 imaginary solutions Zero1 Real Solution

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

Examples 1. 3x 2 +8x=35 3x 2 +8x-35=0 a=3, b=8, c= -35 OR

2. -2x 2 =-2x+3 -2x 2 +2x-3=0 a=-2, b=2, c= -3

Solving Quadratic Equations by the Quadratic Formula Try the following examples. Do your work on your paper and then check your answers.