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
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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_03\090CamAdd_03.cdr Thursday, 3 April 2014 4:46:54 PM BRIAN