Cambridge International Mathematics

3 For each of the following graphs, find the function they represent in the form

y=a(x¡h)^2 +k.

abc

4 Find the quadratic function with:

a vertex(2,¡5) and y-intercept 3 b vertex(¡ 4 ,19) and y-intercept 3

c vertex(1,8) and y-intercept 7 d vertex(¡ 2 ,11) and y-intercept 3

Give your answers in the form f(x)=a(x¡h)^2 +k.

5 Find the quadratic function with:

a vertex(1,¡4) and y-intercept¡ 7 b vertex(¡ 2 ,3) and y-intercept 15

c vertex(¡ 3 ,¡5) and y-intercept 7 d vertex(3,8) and y-intercept¡ 10

Give your answers in the form f(x)=ax^2 +bx+c.

6 Find the quadratic function which has:

a vertex(¡ 2 ,¡5)and passes through(1,13) b vertex(3,¡19)and passes through(¡ 2 ,31)

Give your answers in the form f(x)=a(x¡h)^2 +k:

7 Find the quadratic function which has:

a vertex(¡^32 ,¡ 234 )and passes through(1,¡9)

b vertex(¡ 8 ,135)and passes through(1,¡27).

Give your answers in the form f(x)=ax^2 +bx+c.

8 Find the quadratic function which has:

a x-intercepts¡ 2 and 2 and passes through the point(0,8)

b x-intercepts 1 and 4 and passes through the point(0,¡12)

c x-intercepts¡ 2 and 3 and passes through the point(4,18)

d x-intercepts¡ 4 and 5 and passes through the point(¡ 1 ,36)

e x-intercepts 112 and 3 and passes through the point(1,2)

f x-intercepts¡^34 and^54 and passes through the point(2,33).

We have seen that thex-intercepts of the quadratic functionf(x)=ax^2 +bx+ccorrespond to

the solutions of the equation ax^2 +bx+c=0.

So, we can find the solution to a quadratic equation by graphing the corresponding function

and finding itsx-intercepts. In this section we do this using technology. You can either use

the graphing package provided, or else use the graphics calculator instructions beginning on

page 22.

I USING TECHNOLOGY [2.10]

5

V,()1 ¡3

y

O x

x

y

-1

V,()-2 ¡3

O

-4

V,()-1 -2

y

O x

GRAPHING

PACKAGE

446 Quadratic equations and functions (Chapter 21)

IGCSE01

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Y:\HAESE\IGCSE01\IG01_21\446IGCSE01_21.CDR Monday, 27 October 2008 2:10:05 PM PETER