how to find the function rule

Question

x y 7 56 11 22 16 32 What is the function and how do you find it?

Answer 1

assume y=ax^2 +bx +c . . . for x=7....49a+7b+c=56 . . . for x=11...121a +11b+c=22 . . . for x=16...256a +16b +c=32 . . (121a +11b+c=22) + (-49a -7b -c=-56) giv 72a +4b =-34 . . . (256a +16b+c=32) + (-121a -11b -c=-22) giv 235a+5b=10 . . . or b=(10-235a)/5 . . . plug intu line abuv...72a +4*[(10-235a)/5] =-34 . . . 72a +8 -188a =-34 . . . -116a =-34-8=-42 . . . a=-42/-116=0.362068965 . . . . then b=(10-235a)/5=(10-85.0862069)/5=-75.0862069/5=-15.01724138