Cambridge International Mathematics

y

x

Qw_

x¡=¡2

(\3 ¡2, Er_\)

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17 A stone was thrown from the top of a cliff 60 metres above sea level. The height of the stone

above sea leveltseconds after it was released is given by H(t)=¡ 5 t^2 +20t+60metres.

a Find the time taken for the stone to reach its maximum height.

b What was the maximum height above sea level reached by the stone?

c How long did it take before the stone struck the water?

Review set 21B

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1 Solve forx:

a ¡2(x¡3)^2 =0 b (x+ 5)(x¡4) = 0 c (2¡x)^2 =¡ 1

d x^2 ¡ 5 x=24 e 2 x^2 =8 f 6 x^2 ¡x¡2=0

2 Use the quadratic formula to solve: a x^2 ¡ 4 x=10 b x^2 +x¡9=0

3 Solve forx:

a

x

x+3

=

5

x+7

b

2 x¡ 3

10

=

x¡ 2

x

c

1

x+1

+

3

3 x¡ 5

=1

4 If f(x)=2x^2 +x¡ 2 , find:

a f(1) b f(¡3) c xsuch thatf(x)=4:

5 On the same set of axes, sketch y=x^2 and the function:

a y=¡^12 x^2 b y=(x+2)^2 +5 c y=¡(x¡1)^2 ¡ 3

6 For y=3(x¡2)^2 find the:

aidirection the parabola opens ii y-intercept

iii x-intercepts iv equation of the line of symmetry.

b Sketch a graph of the function showing all of the above features.

7 For y=¡x^2 +7x¡ 10 find the:

aiy-intercept ii x-intercepts

iii equation of the line of symmetry iv coordinates of the vertex.

b Sketch a graph of the function showing all of the above features.

8 The graph of y=a(x¡h)^2 +k is shown alongside.

a Find the value ofh.

b Find the values ofaandkby solving simultaneous equations.

9 Use axes intercepts to sketch the graphs of:

a f(x)=2(x¡3)(x+1) b g(x)=¡x(x+4)

10 The quadratic function f(x)=x^2 +bx+c hasx-intercepts¡ 5 and 3.

Find f(x) in expanded form.

11 The graph of a quadratic function has vertex(2,2), and passes through the point(¡ 1 ,¡7). Find

the function in the form f(x)=a(x¡h)^2 +k:

Quadratic equations and functions (Chapter 21) 453

IGCSE01

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Y:\HAESE\IGCSE01\IG01_21\453IGCSE01_21.CDR Monday, 27 October 2008 2:10:26 PM PETER