Cambridge International Mathematics

Example 8 Self Tutor

If y=2x^2 +4x¡ 5 find the value ofywhen: a x=0 b x=3.

a When x=0,

y= 2(0)^2 + 4(0)¡ 5

=0+0¡ 5

=¡ 5

b When x=3,

y= 2(3)^2 + 4(3)¡ 5

= 2(9) + 12¡ 5

=18+12¡ 5

=25

FINDINGxGIVENy

When we substitute a value fory, we are left with a quadratic equation which we need to solve forx. Since

the equation is quadratic, there may be 0 , 1 or 2 possible values forxfor any one value ofy.

Example 9 Self Tutor

If y=x^2 ¡ 6 x+8 find the value(s) ofxwhen: a y=15 b y=¡ 1

a If y=15 then

x^2 ¡ 6 x+8=15

) x^2 ¡ 6 x¡7=0

) (x+ 1)(x¡7) = 0

) x=¡ 1 or x=7

So, there are 2 solutions.

b If y=¡ 1 then

x^2 ¡ 6 x+8=¡ 1

) x^2 ¡ 6 x+9=0

) (x¡3)^2 =0

) x=3

So, there is only one solution.

EXERCISE 21D

1 Which of the following are quadratic functions?

a y=2x^2 ¡ 4 x+10 b y=15x¡ 8 c y=¡ 2 x^2

d y=^13 x^2 +6 e 3 y+2x^2 ¡7=0 f y=15x^3 +2x¡ 16

2 For each of the following functions, find the value ofyfor the given value ofx:

a y=x^2 +5x¡ 14 when x=2 b y=2x^2 +9x when x=¡ 5

c y=¡ 2 x^2 +3x¡ 6 when x=3 d y=4x^2 +7x+10 when x=¡ 2

3 State whether the following quadratic functions are satisfied by the given ordered pairs:

a f(x)=6x^2 ¡ 10 (0,4) b y=2x^2 ¡ 5 x¡3(4,9)

c y=¡ 4 x^2 +6x (¡^12 ,¡4) d y=¡ 7 x^2 +9x+11 (¡ 1 ,¡6)

e f(x)=3x^2 ¡ 11 x+20 (2,¡10) f f(x)=¡ 3 x^2 +x+6 (^13 ,4)

4 For each of the following quadratic functions, find the value(s) ofxfor the given value ofy:

a y=x^2 +6x+10 when y=1 b y=x^2 +5x+8 when y=2

c y=x^2 ¡ 5 x+1 when y=¡ 3 d y=3x^2 when y=¡ 3 :

430 Quadratic equations and functions (Chapter 21)

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Y:\HAESE\IGCSE01\IG01_21\430IGCSE01_21.CDR Monday, 27 October 2008 2:09:16 PM PETER