Cambridge Additional Mathematics

Quadratics (Chapter 3) 89

4 Find, in the form f(x)=ax^2 +bx+c, the equation of the quadratic whose graph:

a cuts thex-axis at 3 , passes through(5,12), and has axis of symmetry x=2

b cuts thex-axis at 5 , passes through(2,5), and has axis of symmetry x=1.

Example 23 Self Tutor

Find the equation of each quadratic function given its graph:

ab

a Since the vertex is(3,¡2), the

quadratic has the form

y=a(x¡3)^2 ¡ 2 where a> 0.

When x=0, y=16

) 16 =a(¡3)^2 ¡ 2

) 16 = 9a¡ 2

) 18 = 9a

) a=2

The quadratic is y=2(x¡3)^2 ¡ 2.

b Since the vertex is(¡ 4 ,2), the

quadratic has the form

y=a(x+4)^2 +2 where a< 0.

When x=¡ 2 , y=0

) 0=a(2)^2 +2

) 4 a=¡ 2

) a=¡^12

The quadratic is

y=¡^12 (x+4)^2 +2.

5 If V is the vertex, find the equation of the quadratic function with graph:

abc

de f

y

x

V(- 42 , )

-2 O

y

x

16

V,(3 -2)

O

y

x

V() 24 ,

O

V(-) 21 ,

7

O

y

x 1

V() 38 ,

O

y

x

7 x

V(-) 46 ,

O

y

x

V() 23 ,

(3 1),

O

y

x

V&*Qw,-Ew

O

&*Ew,Qw

y

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_03\089CamAdd_03.cdr Thursday, 3 April 2014 4:46:51 PM BRIAN