Step 1:
Vertex $V(1,4)$ open left ward,passing through $P(-2,10)$
Since the parabola opens leftwards,its equation is of the form $Y^2=4aX$
(I.e)$(y-4)^2=-4a(x-1)$
Step 2:
It passes through $(-2,10)$
Therefore $(10-4)^2=-4a(-2-1)$
$\Rightarrow 6^2=12a$
$\Rightarrow 36=12a$
$a=3$
Therefore the equation is $(y-4)^2=-12(x-1)$