In this problem we have that
the transformations are
a vertical dilation of the parent function
the rule is
(x,y) ------> (x,ay)
with a scale factor a
and
a reflection across the x-axis
the rule is
(x,y) -------> (x, -y)
therefore
the function g(x) is equal to
g(x)=-ax^2
Find the value of a
Looking at the graph