Cambridge Additional Mathematics

The axis of symmetry

is midway between

the -intercepts.x

78 Quadratics (Chapter 3)

You should have found thata, the coefficient ofx^2 , controls the width of the graph and whether it opens

upwards or downwards.

For a quadratic function y=ax^2 +bx+c, a 6 =0:

² a> 0 produces the shape called concave up.

a< 0 produces the shape called concave down.

² If ¡ 1 <a< 1 , a 6 =0the graph is wider than y=x^2.

If a<¡ 1 or a> 1 the graph is narrower than y=x^2.

Example 12 Self Tutor

Using axes intercepts only, sketch the graphs of:

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

a y=2(x+ 3)(x¡1)

hasx-intercepts¡ 3 , 1

When x=0,

y= 2(3)(¡1)

=¡ 6

) y-intercept is¡ 6

b y=¡2(x¡1)(x¡2)

hasx-intercepts 1 , 2

When x=0,

y=¡2(¡1)(¡2)

=¡ 4

) y-intercept is¡ 4

c y=^12 (x+2)^2

touchesx-axis at¡ 2

When x=0,

y=^12 (2)^2

=2

) y-intercept is 2

EXERCISE 3D.1

1 Using axes intercepts only, sketch the graphs of:

a y=(x¡4)(x+2) b f(x)=¡(x¡4)(x+2)

c y=2(x+ 3)(x+5) d f(x)=

e f(x)=2(x+3)^2 f y=¡^14 (x+2)^2

2 State the equation of the axis of symmetry for each graph in question 1.

y

O x

12

-4

y

-3 1 x

-6

O

y

x

2

-2O

¡3(x+ 1)(x+5)

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_03\078CamAdd_03.cdr Friday, 17 January 2014 3:58:12 PM BRIAN