The graph of the function f(x) = -2x² - 8x - 12 is attached
Some features of the graph
Investigating the graph shows that the function f(x) = -2x² - 8x - 12 does not have a real root. This is because the graph does not intersect the x axis.
The vertex of the graph, in this case, is the highest position is at coordinates (-2, -4).
They intersect of the graph is shown to be (0, 12).
The graph is attached