We can see that the y-intercept would be (0,-16) since this is the result of replacing x=0 in the function.
We can also find the x-intercepts solving the equation 0=2x^2+4x-16. Doing so, we have:
[tex]\begin{gathered} 0=2x^2+4x-16 \\ 0=x^2+2x-8\text{ (Dividing by 2 on both sides of the equation)} \\ 0=(x+4)(x-2)\text{ (Factoring)} \\ \text{ We can see that the solutions of the equation are x=-4 and x=2} \\ \text{Therefore the x-intercepts are (-4,0) and (2,0)} \end{gathered}[/tex]
The graph that satisfies the conditions we have found previously is the option A.
