We can start with the equation of the parabola in vertex form, as we know the coordinates of the vector:

The vertex is (h,k) = (-5,2), so we get:

We can use another known point, as (-6,4) to calculate the parameter a:

Now that we have no more unknown parameters, we can expland the equation to the standard form:

The equation is y=2x^2+20x+52.