Cambridge International Mathematics

• 2

y

x

@\=\(!\+\2)X\-\5

@\=\!X

• 
  
  
  
  • 55
  
  
  
  

O

+ 2

+ 3

y

x

@\=\(!\-\2)X\+\3

@\=\!X

O

Example 11 Self Tutor

Sketch y=x^2 and y=x^2 +3 on the same set of axes.

Mark the vertex of y=x^2 +3.

We draw y=x^2 and translate

it 3 units upwards, i.e.,

μ

0

3

¶

.

) the vertex is now at(0,3).

Example 12 Self Tutor

Sketch each of the following functions on the same set of axes as y=x^2. In each case state the

coordinates of the vertex.

a y=(x¡2)^2 +3 b y=(x+2)^2 ¡ 5

a We draw y=x^2 and translate it by

μ

2

3

¶

.

The vertex is at(2,3).

b We draw y=x^2 and translate it by

μ

¡ 2

¡ 5

¶

.

The vertex is at(¡ 2 ,¡5).

EXERCISE 21E.2

1 Sketch each of the following functions on the same set of axes as y=x^2 : Use a

separate set of axes for each part, and in each case state the coordinates of the vertex.

a y=x^2 ¡ 3 b y=x^2 ¡ 1 c y=x^2 +1

d y=x^2 ¡ 5 e y=x^2 +5 f y=x^2 ¡^12

2 Sketch each of the following functions on the same set of axes as y=x^2 : Use a separate set of axes

for each part, and in each case state the coordinates of the vertex.

a y=(x¡3)^2 b y=(x+1)^2 c y=(x¡1)^2

d y=(x¡5)^2 e y=(x+5)^2 f y=(x¡^32 )^2

3 Sketch each of the following functions on the same set of axes as y=x^2 : Use a separate set of axes

for each part, and in each case state the coordinates of the vertex.

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

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

x

y

@\=\!X

@\=\!X\+\3

+ 3

• (^3) + 3
  vertex(0' 3)
  O
  GRAPHING
  PACKAGE
  Quadratic equations and functions (Chapter 21) 435
  IGCSE01
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  (^05255075950525507595)
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  Y:\HAESE\IGCSE01\IG01_21\435IGCSE01_21.CDR Monday, 27 October 2008 2:09:32 PM PETER