Given quadratic expression is
[tex]f(x)=-3x^2-4x+7[/tex]Comparing with the general quadratic function
[tex]f(x)=ax^2+bx+c[/tex]We have,
[tex]a=-3,b=-4,c=7[/tex]So, the x coordinate of the vertex is
[tex]\begin{gathered} -\frac{b}{2a}=-\frac{-4}{-6} \\ =-\frac{2}{3} \end{gathered}[/tex]Now, putting the x coordinate in the equation of the given function,we have,
[tex]\begin{gathered} f(-\frac{2}{3})=-3(\frac{4}{9})-4(-\frac{2}{3})+7 \\ =-\frac{12}{9}+\frac{8}{3}+7 \\ =\frac{75}{9} \end{gathered}[/tex]So, the vertex of th egiven quadratic function is at
[tex](-\frac{2}{3},\frac{75}{9})[/tex]