Cambridge Additional Mathematics

If we are given sufficient information on or about a graph, we can determine the quadratic function in

whatever form is required.

Example 20 Self Tutor

Find the equation of the quadratic function with graph:

ab

a Since thex-intercepts are¡ 1 and 3 ,

y=a(x+ 1)(x¡3).

The graph is concave down, so a< 0.

When x=0, y=3

) 3=a(1)(¡3)

) a=¡ 1

The quadratic function is

y=¡(x+ 1)(x¡3).

b The graph touches thex-axis at x=2,

so y=a(x¡2)^2.

The graph is concave up, so a> 0.

When x=0, y=8

) 8=a(¡2)^2

) a=2

The quadratic function is

y=2(x¡2)^2.

Example 21 Self Tutor

Find the equation of the quadratic function with graph:

The axis of symmetry x=1lies midway between thex-intercepts.

) the otherx-intercept is 4.

) the quadratic has the form

y=a(x+ 2)(x¡4) where a< 0

But when x=0, y=16

) 16 =a(2)(¡4)

) a=¡ 2

The quadratic is y=¡2(x+ 2)(x¡4).

E Finding a quadratic from its graph

-2

y

x

x=1

16

O

-2

y

x

x=1

16

3 units 3 units

O

y

x

3

-1 3

O

y

2 x

8

O

Quadratics (Chapter 3) 87

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_03\087CamAdd_03.cdr Thursday, 3 April 2014 4:46:38 PM BRIAN