Answer
$a=6,b=0,c=2$
Work Step by Step
If the vertex of a graph is at (m,n) then the general formula for the quadratic function is $f(x)=a(x-m)^2+n$. According to the picture the vertex of the graph is at (0,2), hence the quadratic function becomes $f(x)=a(x)^2+2$. The point (1,8) is on the graph, hence if we plug in the values we get $8=a+2$, hence a=6, hence $f(x)=6(x)^2+2$, thus $a=6,b=0,c=2$