Cambridge Additional Mathematics

88 Quadratics (Chapter 3)

EXERCISE 3E

1 Find the equation of the quadratic with graph:

abc

de f

2 Find the quadratic with graph:

abc

Example 22 Self Tutor

Find the equation of the quadratic whose graph cuts thex-axis at 4 and¡ 3 , and which passes through

the point (2,¡20). Give your answer in the form y=ax^2 +bx+c.

Since thex-intercepts are 4 and¡ 3 , the quadratic has the form y=a(x¡4)(x+3) wherea 6 =0.

When x=2, y=¡ 20

) ¡20 =a(2¡4)(2 + 3)

) ¡20 =a(¡2)(5)

) a=2

The quadratic is y=2(x¡4)(x+3)

=2(x^2 ¡x¡12)

=2x^2 ¡ 2 x¡ 24

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

a cuts thex-axis at 5 and 1 , and passes through(2,¡9)

b cuts thex-axis at 2 and¡^12 , and passes through(3,¡14)

c touches thex-axis at 3 and passes through(¡ 2 ,¡25)

d touches thex-axis at¡ 2 and passes through(¡ 1 ,4)

y

x

x=-1

-4

4

O

y

x

12

-2 3

O

y

x

4

O 12

y

x

8

O 2

y

x

3

O 1 3

y

x

3

-1 3

O

y

x

x=3

2

12

O

y

x

1

-3

O

y

x

x =-3

-12

O

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_03\088CamAdd_03.cdr Thursday, 3 April 2014 4:46:48 PM BRIAN