Answer :
To calculate the vertex of the parabola you have to use the following formula:
Given the function:
[tex]f(x)=ax^2+bx+c[/tex]The x-coordinate of the vertex can be calculated as:
[tex]x_V=-\frac{b}{2a}[/tex]For the function:
[tex]f(x)=-2x^2-16x-34[/tex]a=-2
b=-16
c=-34
The x-coordinate of the vertex is
[tex]x_V=-\frac{(-16)}{2(-2)}=-4[/tex]The x-coordinate of the vertex is x=-4
Now to calculate the y-coordinate of the vertex you have to replace the formula with the x-coordinate you just obtained:
[tex]\begin{gathered} y_V=f(x_V)=-2(-4)^2-16\cdot(-4)-34 \\ y_V=-32+64-34 \\ y_V=-2 \end{gathered}[/tex]The coordinates of the vertex are (-4,-2) the correct option is the second one.