Answer
$(y-2)^2=\frac{1}{7}(x+1)$
Work Step by Step
Vertex: $V(h,k)=V(-1,2)$
$h=-1$
$k=2$
Equation of a parabola with horizontal axis and vertex at $(h,k)$:
$(y-k)^2=4p(x-h)$
$(y-2)^2=4p(x+1)$
Use the point $(6,1)$:
$(1-2)^2=4p(6+1)$
$1=28p$
$p=\frac{1}{28}$
Finally:
$(y-2)^2=4(\frac{1}{28})(x+1)$
$(y-2)^2=\frac{1}{7}(x+1)$
