4) quadratic functions factorised form

To explore the properties of quadratic functions
and their graphs.
To investigate the factorised form of a
quadratic function.
http://www.youtube.com/watch?v=VSUKNxVXE4E&feature=player_embedded#
http://evmaths.jimdo.com/year11/functions/?logout=1
To be able to express a quadratic into its
different forms.

Factorise the quadratic expression:
Solve the equation

Draw sketch of the function
identify clearly vertex, roots, line of symmetry

can be
expressed as
this expression allows to identify clearly the
roots : x = 3 and x =5
The line of symmetry will be halfway between
the zeros:
The vertex then is at (1 , 16)
imput x=1 into the function to get y

The factorised form of a quadratic function
is useful to determine the zeros (roots) of the
function: x= p and x =q
The line of symmetry will be in the middle of
the two zeros:

Consider the function:
find the zeros:
find the line of symmetry:
find the coordinates of its vertex:
write this function in vertex form:
write this function in general form:

y = (x2)2 y = x 2
+ 1
y = x2
2y = x2
+ 3 y = (x 3 )2
+5
y= 2 x 2
+ 1

y= 3x(x2)
y= x(x2)
y= x(x2)
y= (x1)(x+2)
y= 2(x1)(x+2)

4) quadratic functions factorised form

4) quadratic functions factorised form

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4) quadratic functions factorised form