We have the equation of the quadratic function:
[tex]-x^2+6x-10[/tex]We have to use the vertex formula to calculate the vertex. If h is the x-coordinate of the vertex, we can calculate it as:
[tex]h=\frac{-b}{2a}=\frac{-6}{2\cdot(-1)}=\frac{-6}{-2}=3[/tex]Then, we can calculate the y-coordinate replacing h in the equation:
[tex]\begin{gathered} y_v=-h^2+6h-10=-3^2+6(3)-10 \\ y_v=-9+18-10=-1 \end{gathered}[/tex]The vertex has coordinates (x,y) = (3,-1).
