Answer:
\(x=4\) and \(y=26\)
Explanation:
Since the pattern is \(2;x;12;y\) then
the first differences are as follows:
\(x-2; 12-x; y-12\)
Given that the second difference of the quadratic sequence is 6, then
\[(12-x)-(x-2)=6\]
and
\[(y-12)-(12-x)\]
Solving the first equation:
\(12-x-x+2=6\)
\(14-2x=6\)
\(14-6=2x\)
\(\therefore x=4\)
Solving the second equation:
\((y-12)-(12-x)=6\)
\(y-12-12+x=6\)
\(y-24+4=6\) remember \(x=4\)
\(y=6+24-4\)
\(\therefore y=26\)