Cambridge Additional Mathematics

To find the range of a function on a

given domain, you must evaluate the

function at the endpoints of the domain.

y

x

y=x -6x-2 2

(7 5),

(-2 14),

(3 -11),

O

84 Quadratics (Chapter 3)

2 For each of the following quadratics:

i state the axis of symmetry ii find the coordinates of the vertex

iii find the axes intercepts iv sketch the quadratic v state the range.

a y=x^2 ¡ 8 x+7 b y=¡x^2 ¡ 6 x¡ 8 c f(x)=6x¡x^2

d y=¡x^2 +3x¡ 2 e y=2x^2 +4x¡ 24 f f(x)=¡ 3 x^2 +4x¡ 1

g f(x)=2x^2 ¡ 5 x+2 h y=4x^2 ¡ 8 x¡ 5 i y=¡^14 x^2 +2x¡ 3

3 For each of the following quadratics:

i write the quadratic in factored form and hence find the roots

ii write the quadratic in completed square form and hence find the coordinates of the vertex

iii sketch the quadratic, showing the details you have found.

a y=x^2 ¡ 10 x+16 b y=x^2 +10x+9 c y=x^2 ¡ 14 x+45

4 Sketch the graph of:

a y=

̄

̄x^2 +4x¡ 12

̄

̄ b f(x)=

̄

̄¡x^2 ¡ 3 x+10

̄

̄ c y=

̄

̄ 4 x^2 ¡ 12 x+5

̄

̄

Example 18 Self Tutor

Find the range of y=x^2 ¡ 6 x¡ 2 on the domain ¡ 26 x 67.

y=x^2 ¡ 6 x¡ 2 has a=1, b=¡ 6 , and c=¡ 2.

a> 0 , so the shape is

¡b

2 a

=

¡(¡6)

2(1)

=3

When x=3, y=3^2 ¡6(3)¡ 2

=¡ 11

) the vertex is (3,¡11).

When x=¡ 2 , y=(¡2)^2 ¡6(¡2)¡ 2

=14

When x=7, y=7^2 ¡6(7)¡ 2

=5

So, on the domain fx:¡ 26 x 67 g,

the range is fy:¡ 116 y 614 g.

5 Find the range of:

a f(x)=x^2 +4x¡ 6 on ¡ 66 x 63 b y=¡x^2 +8x+3 on 06 x 67

c y=2x^2 ¡ 12 x+5 on ¡ 26 x 66 d f(x)=7x¡x^2 on ¡ 16 x 65

Activity #endboxedheading

Click on the icon to run a card game for quadratic functions. CARD GAME

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_03\084CamAdd_03.cdr Tuesday, 8 April 2014 10:27:10 AM BRIAN