Answer
$a=6$
$b=0$
$c=2$
Work Step by Step
If the vertex of a graph is at $(m,n)$ then the vertex form for the quadratic function is $f(x)=a(x-m)^2+n$.
The vertex is at $(h,k)=(0,2)$, hence:
$f(x)=a(x-h)^2+k
\\f(x)=a(x-0)^2+2
\\f(x)=ax^2+2$
$(1,8)$ is on the graph, hence plugging in the values into the tentative equation:
$8=a(1)^2+2\\
8=a(1)+2\\
8=a+2\\
a=6$.
Thus, the function is $f(x)=6\cdot x^2+2$.
Therefore, $a=6$, $b=0$, $c=2$.
