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Toexplorethepropertiesofquadraticfunctionsandtheirgraphs.
Toinvestigatethedifferentformsinwhichquadraticfunctionscanbeexpressed.
http://www.youtube.com/watch?v=VSUKNxVXE4E&feature=player_embedded#
http://evmaths.jimdo.com/year11/functions/?logout=1
Sketch the graphs of and
y=x2
y=x22
y=x2+3
vertex:
lineofsymmetry:
vertex:
lineofsymmetry:
Conclusions:
parabola moves upwards
parabola moves downwards
vertex:
line of symmetry:
(0,k)
x=0
Translationk units along yaxis
k>0
k
Trythesetwographsinyourcalculator
y=2x22x4 y=x2+4x3
Whatistheyinterceptineachcase?
Iny=ax2+bx+c
thecoefficientcrepresentstheyinterceptoftheparabola
Stateclearlytheyinterceptoftheseparabolas:
y=x2+1
y=9+5x+x2
y=x2x2
Useyourcalculatortoplotthegraphsof:
y=3x22 y=5x22
y=3 x22
Whatistheeffectofthecoefficienta?
y=5x22
Conclusions:
f(x)=ax2+bx+cThegraphof when
a>0
a
Matcheachformulawithitsgraph
Thegraphshownhasequationy=ax22x+c.Findthevaluesofaandofc.
Thegraphhasequation
Findthevaluesofaandc.
Writethefollowingquadraticfunctionsinthegeneralformy=ax2+bx+c
Statetheyinterceptofeachfunction
xy
Findtherootsofthefollowingfunctions:
Foreachofthefollowingquadraticfunctions
y=2(x3)(x+1)y=3(x1)2+4
(a)Writedowntheyinterceptoftheirgraphs
(b)UseyourGDCtofind(i)thecoordinatesofthevertexontheir
graphs.(ii)theequationofthelineofsymmetry(ii)theroots
(c)Writedownthevalueofaandofb.
SolveEx1Apage5
Attachments
Parabolacanonica.ggb
Cambioscuadratica.ggb
QUADRATICFUNCTIONSI2010.doc
TransformacionesFuncinCuadrtica.ggb
Verticaltranslationofparabola.ggb
Verticalstretchofparabola.ggb
Horizontaltranslationofparabola.ggb
Translationsinparabola.ggb
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Y11 SL EV
QUADRATIC FUNCTIONS
1) Complete
2) Find the minimum value of
3) i) Factorize
ii) Determine the integer values for which
is less than zero.
4) a) Factorise
b) Sketch the graph of
5) Complete
Vertex:
Line of symmetry:
y-intercept:
EMBED Equation.DSMT4
Vertex:
Line of symmetry:
y-intercept:
EMBED Equation.DSMT4
Vertex:
Line of symmetry:
y-intercept:
EMBED Equation.DSMT4
Vertex:
Line of symmetry:
y-intercept:
EMBED Equation.DSMT4
Roots:
Line of symmetry:
Vertex:
y-intercept:
EMBED Equation.DSMT4
Roots:
Line of symmetry:
Vertex:
y-intercept:
EMBED Equation.DSMT4
Roots:
Line of symmetry:
Vertex:
y-intercept:
EMBED Equation.DSMT4
Roots:
Line of symmetry:
Vertex:
y-intercept:
EMBED Equation.DSMT4
_1253110198.unknown
_1253110703.unknown
_1253111211.unknown
_1253111262.unknown
_1253111347.unknown
_1253111234.unknown
_1253110752.unknown
_1253110501.unknown
_1253110535.unknown
_1253110347.unknown
_1253110085.unknown
_1253110145.unknown
_1253109960.unknown
_1253110010.unknown
_1253109856.unknown
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geogebra_javascript.js
function ggbOnInit() {}
geogebra.xml
SMART Notebook
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geogebra_javascript.js
function ggbOnInit() {}
geogebra.xml
SMART Notebook
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geogebra_javascript.js
function ggbOnInit() {}
geogebra.xml
SMART Notebook
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geogebra_javascript.js
function ggbOnInit() {}
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