Cambridge International Mathematics

Example 15 Self Tutor

Find thex-intercepts of:

a y=2(x¡3)(x+2) b y=¡(x¡4)^2

a When y=0,

2(x¡3)(x+2)=0

) x=3 or x=¡ 2

) thex-intercepts are 3 and¡ 2.

b When y=0,

¡(x¡4)^2 =0

) x=4

) thex-intercept is 4.

FACTORISING TO FINDx-INTERCEPTS

For any quadratic function of the formy=ax^2 +bx+c, thex-intercepts

can be found by solving the equation ax^2 +bx+c=0.

We saw earlier in the chapter that quadratic equations may havetwo solutions,one solution,orno solutions.

These solutions correspond to thetwox-intercepts,onex-intercept,ornox-interceptsfound when the graphs

of the quadratic functions are drawn.

Example 16 Self Tutor

Find thex-intercept(s) of the quadratic functions:

a y=x^2 ¡ 6 x+9 b y=¡x^2 ¡x+6

a When y=0, x^2 ¡ 6 x+9=0

) (x¡3)^2 =0

) x=3

) thex-intercept is 3.

b When y=0, ¡x^2 ¡x+6=0

) x^2 +x¡6=0

) (x+ 3)(x¡2) = 0

) x=¡ 3 or 2

) thex-intercepts are¡ 3 and 2.

EXERCISE 21F.1

1 For the following functions, state they-intercept:

a y=x^2 +3x+3 b y=x^2 ¡ 5 x+2 c y=2x^2 +7x¡ 8

d y=3x^2 ¡x+1 e y=¡x^2 +3x+6 f y=¡ 2 x^2 +5¡x

g y=6¡x¡x^2 h y=8+2x¡ 3 x^2 i y=5x¡x^2 ¡ 2

2 For the following functions, find thex-intercepts:

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

d y=¡3(x¡4)(x¡5) e y=2(x+3)^2 f y=¡5(x¡1)^2

If a quadratic

function has only

one -intercept then

its graph must

the -axis.

x

touch x

yx¡=¡¦()

2 solutions

yx¡=¡¦()

1 solution

yx¡=¡¦()

0 solutions

Quadratic equations and functions (Chapter 21) 439

IGCSE01

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Y:\HAESE\IGCSE01\IG01_21\439IGCSE01_21.CDR Monday, 27 October 2008 2:09:44 PM PETER