Explanation:
Here you haven't provided any function, so I'll assume this one:
[tex]f(x)=3x^2-18x+33[/tex]
This is a quadratic function whose graph represents a parabola. Any parabola has its vertex at the point:
[tex]V(x,y) \\ \\ \\ x=-\frac{b}{2a} \\ \\ y=f(-\frac{b}{2a}) \\ \\ \\ where: \\ \\ \\ f(x)=ax^2+bx+c \\ \\ \\ So: \\ \\ a=3 \\ \\ b=-18 \\ \\ c=33[/tex]
Therefore:
[tex]x=-\frac{(-18)}{2(3)}=3 \\ \\ f(3)=3(3)^2-18(3)+33=27-54+33=6[/tex]
Therefore, the vertex is:
[tex]\boxed{V(3,6)}[/tex]
