Cambridge International Mathematics

Part 2: Graphs of the form y=(x¡h)^2

What to do:

1 Using agraphing packageorgraphics calculator:

i graph the two functions on the same set of axes

ii state the coordinates of the vertex of each function.

a y=x^2 and y=(x¡2)^2 b y=x^2 and y=(x+2)^2

c y=x^2 and y=(x¡4)^2 d y=x^2 and y=(x+4)^2

2 What effect does the value ofhhave on:

a the position of the graph b the shape of the graph?

3 What transformation is needed to graph y=(x¡h)^2 from y=x^2?

Part 3: Graphs of the form y=(x¡h)^2 +k

What to do:

1 Without the assistance of technology, sketch the graph of y=(x¡2)^2 +3.

State the coordinates of the vertex and comment on the shape of the graph.

2 Use agraphing packageorgraphics calculatorto draw, on the same set of axes, the graphs of

y=x^2 and y=(x¡2)^2 +3:

3 Repeat steps 1 and 2 for y=(x+4)^2 ¡ 1.

4 Copy and complete:

² The graph of y=(x¡h)^2 +k is the same shape as the graph of ......

² The graph of y=(x¡h)^2 +k is a ................ of the graph ofy=x^2

through a translation of ........

Part 4: Graphs of the form y=ax^2 , a 6 =0

What to do:

1 Using agraphing packageorgraphics calculator:

i graph the two functions on the same set of axes

ii state the coordinates of the vertex of each function.

a y=x^2 and y=2x^2 b y=x^2 and y=4x^2

c y=x^2 and y=^12 x^2 d y=x^2 and y=¡x^2

e y=x^2 and y=¡ 2 x^2 f y=x^2 and y=¡^12 x^2

2 These functions are all members of the family y=ax^2 whereais the coefficient of thex^2

term. What effect doesahave on:

a the position of the graph b the shape of the graph

c the direction in which the graph opens?

Quadratic equations and functions (Chapter 21) 433

IGCSE01

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Y:\HAESE\IGCSE01\IG01_21\433IGCSE01_21.CDR Monday, 27 October 2008 2:09:26 PM PETER