Cambridge Additional Mathematics

90 Quadratics (Chapter 3)

Discovery 3 Finding quadratic functions

x 0 1 2 3 4 5

y 7 12 21 34 51 72

For the quadratic functiony=2x^2 +3x+7we can find

a table of values for x=0, 1 , 2 , 3 , 4 , 5.

x 0 1 2 3 4 5

y 7 12 21 34 51 72

¢ 1 5 9 13 17 21

¢ 2 4444

9 ¡ 534 ¡ 21 72 ¡ 51

We turn this table into adifference tableby adding two

further rows:

² the row¢ 1 gives the differences between successive

y-values

² the row¢ 2 gives the differences between successive

¢ 1 -values.

What to do:

1 Construct difference tables for x=0, 1 , 2 , 3 , 4 , 5 for each of the following quadratic functions:

a y=x^2 +4x+3 b y=3x^2 ¡ 4 x

c y=5x¡x^2 d y=4x^2 ¡ 5 x+2

2 What do you notice about the¢ 2 row for each of the quadratic functions in 1?

3 Consider the general quadratic y=ax^2 +bx+c, a 6 =0.

a Copy and complete the following difference table:

x 01 2 345

y °ca+b+c 4 a+2b+c :::::: :::::: ::::::

¢ 1 ° :::::: :::::: :::::: ::::::

¢ 2 ° :::::: :::::: ::::::

b Comment on the¢ 2 row.

c What can the encircled numbers be used for?

4 Use your observations in 3 to determine, if possible, the quadratic functions with the following

tables of values:

a x^01234

y 6 5 8 15 26

b x^01234

y 8 10 18 32 52

c x 0 1 2 3 4

y 1 2 ¡ 1 ¡ 8 ¡ 19

d x 0 1 2 3 4

y 5 3 ¡ 1 ¡ 7 ¡ 15

5 We wish to determine themaximumnumber of pieces into which a pizza can be cut usingncuts

across it.

For example, for n=1we have which has 2 pieces

for n=3we have which has 7 pieces.

1 2 1 2 3 4

5

6

7

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_03\090CamAdd_03.cdr Thursday, 3 April 2014 4:46:54 PM BRIAN