Cambridge International Mathematics

-2 6

x

y

x¡=¡2

2

O

y

x

x= 1

3

-1 3

vertex(1' 4)

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

O

c Fromb, when x=1,

y=¡(1)^2 + 2(1) + 3

=¡1+2+3

=4

) the vertex is(1,4).

d

Example 22 Self Tutor

a Sketch the graph of y=2(x¡2)(x+4) using axes intercepts.

b Find the equation of the line of symmetry and the coordinates of the vertex.

a Since a=2 the parabola opens upwards

When x=0,

y=2£¡ 2 £4=¡ 16

) y-intercept is¡ 16.

When y=0,

2(x¡2)(x+4)=0

) x=2 or x=¡ 4

) thex-intercepts are 2 and¡ 4.

b The line of symmetry is halfway between thex-intercepts

) since¡ 1 is the average of¡ 4 and 2 ,

the line of symmetry isx=¡ 1

When x=¡ 1 , y=2(¡ 1 ¡2)(¡1+4)

=2£¡ 3 £ 3

=¡ 18

) the vertex is(¡ 1 ,¡18).

Example 23 Self Tutor

Sketch the parabola which hasx-intercepts¡ 2 and 6 , andy-intercept 2.

Find the equation of the line of symmetry.

The line of symmetry lies half-way between the

x-intercepts.

The average of¡ 2 and 6 is 2 , so the line of

symmetry isx=2.

x

y

• 4 2
  
  
  • 16
  
  
  
  

!\=\-1

V(-1' -18)

O

Quadratic equations and functions (Chapter 21) 443

IGCSE01

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