Cambridge International Mathematics

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Example 10 Self Tutor

Draw the graph of y=x^2 +2x¡ 3 from a table of values fromx=¡ 3 tox=3.

Consider f(x)=x^2 +2x¡ 3

Now, f(¡3) = (¡3)^2 +2(¡3)¡ 3

=9¡ 6 ¡ 3

=0

We can do the same for the other values ofx.

Tabled values are:

x ¡ 3 ¡ 2 ¡ 1 0 1 2 3

y 0 ¡ 3 ¡ 4 ¡ 3 0 5 12

EXERCISE 21E.1

1 From a table of values for x=¡ 3 ;¡ 2 ,¡ 1 , 0 , 1 , 2 , 3 draw the graph of:

a y=x^2 ¡ 2 x+8 b y=¡x^2 +2x+1 c y=2x^2 +3x

d y=¡ 2 x^2 +4 e y=x^2 +x+4 f y=¡x^2 +4x¡ 9

2 Use agraphing packageorgraphics calculatorto check your graphs in question 1.

Discovery 1 Graphs of quadratic functions

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In this discovery we consider different forms of quadratic functions, and how the form of the quadratic

affects its graph.

Part 1: Graphs of the form y=x^2 +k wherekis a constant

What to do:

1 Using agraphing packageorgraphics calculator:

i graph the two functions on the same set of axes

ii state the coordinates of the vertex of each function.

a y=x^2 and y=x^2 +2 b y=x^2 and y=x^2 ¡ 2

c y=x^2 and y=x^2 +4 d y=x^2 and y=x^2 ¡ 4

2 What effect does the value ofkhave on:

a the position of the graph b the shape of the graph?

3 What transformation is needed to graph y=x^2 +k from y=x^2?

GRAPHING

PACKAGE

GRAPHING

PACKAGE

432 Quadratic equations and functions (Chapter 21)

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Y:\HAESE\IGCSE01\IG01_21\432IGCSE01_21.CDR Monday, 10 November 2008 12:27:46 PM PETER