What is the equation of the blue graph

Hmm, we can't really see where the x intercept are

oh, look, we all the answers are in vertex form
so

vertex form is
g(x)=a(x-h)²+k
where (h,k) is teh vertex
and a is some constant

we see that the vertex is at (1,-3) so
h=1, k=-3

g(x)=a(x-1)²-3 is da equation
we see that all the choices have a=1 so
g(x)=(x-1)²-3

so answer is C