Question 120149
the differences in x are constant (2)


the differences in y are 5, 7, 9, 11 __ but the differences in the differences are constant (2)


this indicates a second order (squared) relation


y=ax^2+bx+c


for (2,3) 3=4a+2b+c
for (4,8) 8=16a+4b+c
for (6,15) 15=36a+6b+c


subtracting first from second gives 5=12a+2b (A)
subtracting second from third gives 7=20a+2b (B)


subtracting (A) from (B) gives 2=8a, so a=.25


substituting gives 5=12(.25)+2b __ 2=2b __ 1=b


substituting gives 3=4(.25)+2(1)+c __ 3=1+2+c __ 0=c


y=.25x^2+x