First, let's compare the given equation with the standard form of a quadratic equation, so we can find the parameters a, b and c:
[tex]\begin{gathered} y=ax^2+bx+c\\ \\ y=-2x^2-4x+7\\ \\ a=-2,b=-4,c=7 \end{gathered}[/tex]
The value of a indicates if the graph opens upward or downward:
a > 0: graph opens upward.
a < 0: graph opens downward.
Since a = -2 is negative, the graph opens downward.
Also, if the graph opens downward, the vertex of the graph is a maximum point.
Therefore the correct option is the third one.
