Answer
a)
x $x^2-3$ $3x^2$ $4x^2-5x$
1 -2 3 -1
2 1 12 6
3 6 27 21
4 13 48 44
5 22 75 75
Common differences are below.
From left to right (for the formulas above), the common differences are 2, 6, and 8.
b) The relationship is that the difference is twice the coefficient of the $x^2$ term.
c) The next terms in the quadratic formulas can be determined by extending these differences.
Work Step by Step
a)
$1--2=3$
$6-1 =5$
$13-6 = 7$
$22-13= 9$
$5-3=2$
$7-5=2$
$9-7=2$
$12-3=9$
$27-12= 15$
$48-27=21$
$75-48=27$
$15-9=6$
$21-15=6$
$27-21=6$
$6--1=7$
$21-6=15$
$44-21=23$
$75-44=31$
$15-7=8$
$23-15=8$
$31-23=8$
