Cambridge International Mathematics

EXERCISE 21E.3

1 On separate sets of axes sketch y=x^2 and each of the following functions.

Comment on:

i the shape of the graph ii the direction in which the graph opens.

a y=5x^2 b y=¡ 5 x^2 c y=^13 x^2

d y=¡^13 x^2 e y=¡ 4 x^2 f y=^14 x^2

2 Sketch the graphs of the following functions without using tables of values and state the

coordinates of their vertices:

a y=¡(x¡1)^2 +3 b y=2x^2 +4 c y=¡(x¡2)^2 +4

d y=3(x+1)^2 ¡ 4 e y=^12 (x+3)^2 f y=¡^12 (x+3)^2 +1

g y=¡2(x+4)^2 +3 h y=2(x¡3)^2 +5 i y=^12 (x¡2)^2 ¡ 1

3 Match each quadratic function with its corresponding graph:

a y=¡1(x+1)^2 +3 b y=¡2(x¡3)^2 +2 c y=x^2 +2

d y=¡1(x¡1)^2 +1 e y=(x¡2)^2 ¡ 2 f y=^13 (x+3)^2 ¡ 3

g y=¡x^2 h y=¡^12 (x¡1)^2 +1 i y=2(x+2)^2 ¡ 1

ABC

DEF

GH I

4

a y=2x^2 and y=2x^2 ¡ 3 x+1 b y=¡x^2 and y=¡x^2 ¡ 6 x+4

c y=3x^2 and y=3x^2 ¡ 5 x d y=¡ 2 x^2 and y=¡ 2 x^2 +5

GRAPHING

PACKAGE

3

3

x

y

O

• 4

2

x

y

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4

2

x

y

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• 2

3

x

y

O

3

4 x

y

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2

x

y

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• 2

1

x

y

O

• 3

2 x

y

O

• 6
  
  
  • 3
  
  
  
  

x

y

O

Use a or to graph each pair of quadratic

functions on the same set of axes. Compare the shapes of the two graphs.

graphing package graphics calculator GRAPHING

PACKAGE

Quadratic equations and functions (Chapter 21) 437

IGCSE01

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Y:\HAESE\IGCSE01\IG01_21\437IGCSE01_21.CDR Monday, 27 October 2008 2:09:38 PM PETER