Cambridge International Mathematics

x

y

• 12

4

O

3 For the following functions, find thex-intercepts:

a y=x^2 ¡ 9 b y=2x^2 ¡ 6 c y=x^2 +7x+10 d y=x^2 +x¡ 12

e y=4x¡x^2 f y=¡x^2 ¡ 6 x¡ 8 g y=¡ 2 x^2 ¡ 4 x¡ 2 h y=x^2 ¡ 6 x+9

i y=x^2 ¡ 4 x+1 j y=x^2 +4x¡ 3 k y=x^2 ¡ 6 x¡ 2 l y=x^2 +8x+11

GRAPHS FROM AXES INTERCEPTS

If we know thexandy-intercepts of a quadratic function then we can use them to draw its graph.

Example 17 Self Tutor

Sketch the graphs of the following functions by considering:

i the value ofa ii they-intercept iii thex-intercepts.

a y=x^2 ¡ 2 x¡ 3 b y=¡2(x+ 1)(x¡2)

Example 18 Self Tutor

Sketch the graph of y=2(x¡3)^2 by considering:

a the value ofa b they-intercept c thex-intercepts.

a a=2, so the parabola opens upwards

b y-intercept occurs whenx=0

) y= 2(0¡3)^2 =18

) they-intercept is 18

c x-intercepts occur wheny=0

) 2(x¡3)^2 =0

) x=3

) thex-intercept is 3

There is only onex-intercept, which means the graphtouchesthex-axis.

3

• 3


• 1

x

y

O

x

y

18

O^3

aia=1, so the parabola opens upwards

ii y-intercept occurs when x=0

) they-intercept is¡ 3

iii x-intercepts occur wheny=0

) x^2 ¡ 2 x¡3=0

) (x¡3)(x+1)=0

) x=3 or x=¡ 1

) thex-intercepts are 3 and¡ 1

Sketch:

bia=¡ 2 , so the parabola opens downwards

ii y-intercept occurs when x=0

) y=¡2(0 + 1)(0¡2)

=¡ 2 £ 1 £¡2=4

) they-intercept is 4

iii x-intercepts occur wheny=0

) ¡2(x+ 1)(x¡2) = 0

) x=¡ 1 or x=2

) thex-intercepts are¡ 1 and 2

Sketch:

440 Quadratic equations and functions (Chapter 21)

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Y:\HAESE\IGCSE01\IG01_21\440IGCSE01_21.CDR Monday, 27 October 2008 2:09:47 PM PETER