9.5SolvingQuadraticEquationsUsingtheQuadraticFormula

ThenotoriousQUADRATICFORMULA!!!!

! = −$ ± $& − 4()2(

Example1:UsingtheQuadraticFormulaSolve2!& − 5! + 3 = 0usingthequadraticformulaExample2:ModelingwithmathematicsThenumberyofNorthernRockyMountainwolfbreedingpairsxyearssince1990canbemodeledbythefunction/ = 0.20!& + 1.8! − 3.Whenwerethereabout35breedingpairs?TheDiscriminant

$& − 4()inthequadraticformulaiscalledthediscriminant

Example3:Determiningthenumberofrealsolutionsa) Determinethenumberofrealsolutionsof!& + 8! − 3 = 0

b) Determinethenumberofrealsolutionsof9!& + 1 = 6!Example4:FindingtheNumberofx-interceptsofaParabolaFindthenumberofx-interceptsofthegraphof/ = 2!& + 3! + 9.SpiralReview:

Method Advantages DisadvantagesFactoring

Graphing

Usingsquareroots

Completingthesquare

QuadraticFormula

Example5:ChoosingaMethodSolveeachequationusinganymethod.Explainyourchoiceofmethod.

a) !& − 10! = 1Method:_______________

b) 2!& − 13! − 24 = 0Method:_______________

c) !& + 8! + 12 = 0Method:_______________

Homework:5,9,10,15,22,23,25,27,37-43odd,50,62