Given:
The equation of the parabola is

To find:
The vertex and check whether it opens up or down.
Solution:
We have,

Here, leading coefficient is 2 which is a positive number. So, the parabola opens up.
The vertex of parabola
is

Here, a=2, b=8 and c=3.



Putting x=-2 in the given equation.




So, the vertex of the parabola is at (-2,-5) and parabola opens up.
Therefore, the correct option is D.