2) quadratics gral form

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

geogebra_thumbnail.png

geogebra.xml

SMART Notebook

geogebra_thumbnail.png

geogebra.xml

SMART Notebook

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

SMART Notebook

geogebra_thumbnail.png

geogebra.xml

SMART Notebook

geogebra_thumbnail.png

geogebra_javascript.js

function ggbOnInit() {}

geogebra.xml

SMART Notebook

geogebra_thumbnail.png

geogebra_javascript.js

function ggbOnInit() {}

geogebra.xml

SMART Notebook

geogebra_thumbnail.png

geogebra_javascript.js

function ggbOnInit() {}

geogebra.xml

SMART Notebook

geogebra_thumbnail.png

geogebra_javascript.js

function ggbOnInit() {}

geogebra.xml

SMART Notebook

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