As given by the question
There are given that the vertex of the parabola is, (-5, -2), x = -4, y = 2.
Now,
From the vertex,

vertex form of the parabola is:

Substitute the value of x, y, h, and k into the equation (1)
Then,

Then,
Substitute the value of a=4 into the equation (1)

So,
The coefficient of the squared expression in the parabola equation is 4
Hence, the correct option is C.