1. 1
Sep 26­04:59 p.m.
To explore the properties of quadratic functions
and their graphs.
To investigate the different forms in which
quadratic functions can be expressed.
To explore the transformations of quadratic
functions and their graphs.
http://www.youtube.com/watch?v=VSUKNxVXE4E&feature=player_embedded#
http://evmaths.jimdo.com/year­11/functions/?logout=1

2. 2
Sep 26­04:59 p.m.
f(x) = x2
vertex:
line of symmetry:

3. 3
Sep 26­04:59 p.m.
What do you expect if ?
y = x2
y = ­ x2
vertex:
line of symmetry:

4. 4
Sep 26­04:59 p.m.
Draw , and
y = x2 y = 2 x2
vertex:
line of symmetry:

5. 5
Sep 26­04:59 p.m.
Conclusions:
y = a x 2
The graph of is a parabola with
vertex: (0,0) line of symmetry : x = 0
a > 0 a < 0
|a | > 1 as "a" increases the parabola gets "thinner"
0 < |a| <1 the parabola looks "fatter"
"a " produces a stretch along the y-axis

6. 6
Sep 26­04:59 p.m.
Sketch the graphs of and
vertex:
line of symmetry:
vertex:
line of symmetry:
y = ( x + 3)2
y = ( x ­ 2 )2
y = x2

7. 7
Sep 26­04:59 p.m.
Conclusions:
parabola moves to the right
parabola moves to the left
vertex:
line of symmetry:
vertex:
line of symmetry:
( h , 0 )
x = h
( ­ h , 0 )
x = ­ h
Translation along x­axis
( h > 0 )

8. 8
Sep 26­04:59 p.m.
Sketch the graphs of and
y=x2
y=x2
­2
y=x2
+3
vertex:
line of symmetry:
vertex:
line of symmetry:

9. 9
Sep 26­04:59 p.m.
Conclusions:
parabola moves upwards
parabola moves downwards
vertex:
line of symmetry:
( 0 , k )
x = 0
Translation k units along
y­axis
k > 0
k < 0

10. 10
Sep 26­04:59 p.m.
Conclusions: vertex
(h , k)
(­h , k)
In general:
represents a parabola
• with vertex in (h,k)
• axis of symmetry x = h
• a produces a stretch parallel to the y- axis
• a > 0
• a < 0

11. 11
Sep 26­04:59 p.m.
y = ( x ­ 1 ) 2
+ 3
vertex:
line of symmetry:
y = 2 ( x ­ 3 ) 2
vertex:
line of symmetry:
(1,3)
x=1
(3,0)
x=3

12. 12
Sep 26­04:59 p.m.
y = ­ 3 x2
+ 4
vertex:
line of symmetry:
y = 3 ( x + 1 ) 2
­ 2
vertex:
line of symmetry:
(0,4)
x=0
(-1,-2)
x=-1
http://members.shaw.ca/ron.blond/QFA.CSF.APPLET/index.html
Transformaciones Función Cuadrática.ggb

13. 13
Sep 26­04:59 p.m.
For
Parabolas of the form
What is the y­intercept ?
Find the roots of f.
Concavity?
factorising (if possible)
by formula
(y = 0)

14. 14
Sep 26­04:59 p.m.
y­intercept = ­8
roots : ­ 4 and 2
line of symmetry?
vertex?

15. 15
Sep 26­04:59 p.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 )
a < 0a >0
Cambios cuadratica.ggb

16. 16
Sep 26­04:59 p.m.
For find:
y- intercept:
line of symmetry:
vertex:
roots:
Now draw a sketch of the function.

17. 17
Sep 26­04:59 p.m.
y- intercept: line of symmetry:
vertex: roots:
Now draw a sketch of the function.
Express f(x) in the form

18. 18
Sep 26­04:59 p.m.
y = a (x ­ x1) ( x ­ x2)Parabolas of the form :
y = ( x ­ 3 ) ( x + 1 )
Roots:
Line of symmetry:
Vertex:
In general:
x1 and x2

19. 19
Sep 26­04:59 p.m.
axis of symmetry
vertex
root
root
y­ intercept
(0 , c )

20. 20
Sep 26­04:59 p.m.
y = (x­2)2
y = ­ x 2
+ 1
y = x2
­ 2
y = x2
+ 3
y = (x ­ 3 )2
+5
y= ­ 2 x 2
+ 1

21. Attachments
Parabola canonica.ggb
Cambios cuadratica.ggb
QUADRATIC FUNCTIONS I 2010.doc
Transformaciones Función Cuadrática.ggb