You have the following function:
[tex]g(x)=2x^2-4x-16[/tex]
the x coordinate of the vertex is given by:
[tex]x=-\frac{b}{2a}[/tex]
in this case, a = 2 and b = -4. Replace these values into the previous expression and simplify:
[tex]x=-\frac{-4}{2(2)}=1[/tex]
next, replace the previous values of x into the function g(x):
[tex]\begin{gathered} g(1)=2(1)^2-4(1)-16 \\ g(1)=-18 \end{gathered}[/tex]
then, the vertex is (1,-18)
In order to graph, calculate another point for any value of x, for instance, for x = 0:
g(0) = 2(0)^2 - 4(0) - 16
