Cambridge International Mathematics

y

x

+ 2

• 3

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

@\=\-!X

@\=\!X

()2 -3,

OO

x

y

@\=\!X

@\=\3!X

@\=\-3!X

OO

Example 13 Self Tutor

Sketch y=x^2 on a set of axes and hence sketch:

a y=3x^2 b y=¡ 3 x^2

a y=3x^2 is ‘thinner’ thany=x^2 :

b y=¡ 3 x^2 is the same shape as

y=3x^2 but opens downwards.

Example 14 Self Tutor

Sketch the graph of y=¡(x¡2)^2 ¡ 3 from the graph of y=x^2 and

hence state the coordinates of its vertex.

y=¡(x¡2)^2 ¡ 3

reflect in

x-axis

horizontal shift

2 units right

vertical shift

3 units down

The vertex is at(2,¡3).

Consider the quadratic function y=3(x¡1)^2 +2.

y=3(x¡1)^2 +2

a=3 h=1 k=2

This graph has the same shape as the graph of

y=3x^2 but with vertex ( 1 , 2 ).

On expanding: y=3(x¡1)^2 +2

) y=3(x^2 ¡ 2 x+1)+2

) y=3x^2 ¡ 6 x+3+2

) y=3x^2 ¡ 6 x+5

From this we can see that:

the graph of a quadratic of the form y=ax^2 +bx+c has the same shape as the graph of y=ax^2.

x

y

@\=\3(!\-\1)X\+\2

@\=\3!X V(1'\2)

5

O

436 Quadratic equations and functions (Chapter 21)

GRAPHS WHEN THE LEADING COEFFICIENT 6 =1

IGCSE01

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Y:\HAESE\IGCSE01\IG01_21\436IGCSE01_21.CDR Tuesday, 18 November 2008 12:03:49 PM PETER