Cambridge Additional Mathematics

Quadratics (Chapter 3) 83

To graph a quadratic of the form y=ax^2 +bx+c, we:

² find the axis of symmetry x=¡b

2 a

² substitute to find they-coordinate of the vertex

² state they-interceptc

² find thex-intercepts by solving ax^2 +bx+c=0, either by factorisation or using the quadratic

formula.

Example 17 Self Tutor

Consider the quadratic f(x)=2x^2 +8x¡ 10.

a Find the axis of symmetry. b Find the coordinates of the vertex.

c Find the axes intercepts. d Hence, sketch the function.

e State the range of the function.

f(x)=2x^2 +8x¡ 10 has a=2, b=8, and c=¡ 10.

a> 0 , so the shape is

a

¡b

2 a

=

¡ 8

2(2)

=¡ 2

The axis of symmetry is x=¡ 2.

b f(¡2) = 2(¡2)^2 +8(¡2)¡ 10

=¡ 18

The vertex is (¡ 2 ,¡18).

c They-intercept is¡ 10.

When y=0, 2 x^2 +8x¡10 = 0

) 2(x^2 +4x¡5) = 0

) 2(x+ 5)(x¡1) = 0

) x=¡ 5 or 1

) thex-intercepts are¡ 5 and 1.

d

e The range is fy:y>¡ 18 g.

EXERCISE 3D.3

1 Locate the turning point or vertex for each of the following quadratic functions:

a f(x)=x^2 ¡ 4 x+2 b y=x^2 +2x¡ 3

c y=2x^2 +4 d f(x)=¡ 3 x^2 +1

e y=2x^2 +8x¡ 7 f f(x)=¡x^2 ¡ 4 x¡ 9

g y=2x^2 +6x¡ 1 h f(x)=2x^2 ¡ 10 x+3

i y=¡^12 x^2 +x¡ 5

The vertex lies on the

axis of symmetry.

y

-5 1 x

-10

x=-2

(-2 -18),

O

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_03\083CamAdd_03.cdr Friday, 17 January 2014 3:58:59 PM BRIAN