1. 1Sep2604:59p.m.To explore the properties of quadratic functionsand their graphs.To investigate the different forms in whichquadratic functions can be expressed.To explore the transformations of quadraticfunctions and their graphs.http://www.youtube.com/watch?v=VSUKNxVXE4E&feature=player_embedded#http://evmaths.jimdo.com/year11/functions/?logout=1

2. 2Sep2604:59p.m.f(x)=x2vertex:lineofsymmetry: 3. 3Sep2604:59p.m.Whatdoyouexpectif?y=x2y=x2vertex:lineofsymmetry: 4. 4Sep2604:59p.m.Draw,andy=x2 y=2x2vertex:lineofsymmetry: 5. 5Sep2604:59p.m.Conclusions:y=ax2The graph of is a parabola withvertex: (0,0) line of symmetry : x=0a>0 a1 as "a" increases the parabola gets "thinner"00k 0 a < 0 11. 11Sep2604:59p.m.y=(x1)2+3vertex:line of symmetry:y=2(x3)2vertex:line of symmetry:(1,3)x=1(3,0)x=3 12. 12Sep2604:59p.m.y=3x2+4vertex:line of symmetry:y=3(x+1)22vertex:line of symmetry:(0,4)x=0(-1,-2)x=-1http://members.shaw.ca/ron.blond/QFA.CSF.APPLET/index.htmlTransformacionesFuncinCuadrtica.ggb 13. 13Sep2604:59p.m.ForParabolas of the formWhatistheyintercept?Findtherootsoff.Concavity?factorising (if possible)by formula(y=0) 14. 14Sep2604:59p.m.yintercept=8roots:4and2lineofsymmetry?vertex? 15. 15Sep2604:59p.m.Line of symmetry is in the middle between the roots :The vertex will be on the line of symmetry:We can also find the line of symmetry by doing :y - intercept: (0,c)a0Cambioscuadratica.ggb 16. 16Sep2604:59p.m.For find:y- intercept:line of symmetry:vertex:roots:Now draw a sketch of the function. 17. 17Sep2604:59p.m.y- intercept: line of symmetry:vertex: roots:Now draw a sketch of the function.Express f(x) in the form 18. 18Sep2604:59p.m.y=a(xx1)(xx2)Parabolas of the form :y=(x3)(x+1)Roots:Lineofsymmetry:Vertex:In general:x1andx2 19. 19Sep2604:59p.m.axisofsymmetryvertexrootrootyintercept(0,c) 20. 20Sep2604:59p.m.y=(x2)2y=x2+1y=x22y=x2+3y=(x3)2+5y=2x2+1 21. AttachmentsParabolacanonica.ggbCambioscuadratica.ggbQUADRATICFUNCTIONSI2010.docTransformacionesFuncinCuadrtica.ggb