canonic form of a quadratic, completed square form

1. To explore the properties of quadratic functions
and their graphs.
To investigate the different forms in which
quadratic functions can be expressed.
To express a quadratic function in vertex form.
http://www.youtube.com/watch?v=VSUKNxVXE4E&feature=player_embedded#
http://evmaths.jimdo.com/year­11/functions/?logout=1

2. Draw sketches of these quadratic functions
with the help of your calculator and state
the vertex in each case,
V=
V=
V=
V=

3. is called Vertex Form or completed square form
A quadratic function y = a (x ­ h )2
+ k has its
vertex in (h , k) and line of symmetry x = h.

4. Let's go back to the examples:
V= (5 , 3)
write this quadratic in general form, thus find
a, b and c
line of symmetry: x = 5
a =2 b = ­ 20 c = 53
line of symmetry:

5. Let's go back to the examples:
V= (­5 , 3)
write this quadratic in general form, thus find
a, b and c
line of symmetry: x = ­5
a =1 b = 10 c = 28
line of symmetry:

6. Let's go back to the examples:
V= (2 , 7)
write this quadratic in general form, thus find
a, b and c
line of symmetry: x = 2
a = ­3 b = 12 c = ­ 5
line of symmetry:

7. a)Write the function y = ­ x2
+ 4 x ­ 3 in the
form y =a( x ­ h )2
+k , hence state its maximum
point.
b) Solve the equation y = ­ 8
a= ­1, b= 4 , c =­ 3
line of symmetry: x =2
vertex or maximum point will be when x = 2
when x = 2 then y = ­(2)2
+4(2)­3= 1
so V = ( 2, 1)

8. b) Solve the equation y = ­ 8

9. Find the equation of the quadratic function
represented in the graph
and passes through (0,­11)

10. Solve Ex 1 B page 11