we have the function
f(x)=3x^2-54x+241
this is a vertical parabola open upward (because the leading coefficient is positive)
the vertex is a minimum
Convert the quadratic equation into vertex form
y=a(x-h)^2+k
where
(h,k) is the vertex
and the axis of symmetry is equal to the x-coordinate of the vertex
so
x=h
step 1
Factor the leading coefficient
![\begin{gathered} f(x)=3(x^2-18x)+241 \\ \text{complete the squares} \\ f(x)=3(x^2-18x+9^2-9^2)+241 \\ f(x)=3(x^2-18x+9^2)+241-(9^2)\cdot(3) \\ f(x)=3(x^2-18x+81)+241-243 \\ \text{rewrite as p}\operatorname{erf}ect\text{ squares} \\ f(x)=3(x-9)^2-2 \end{gathered}]()
the vertex is the point (9,-2)
the axis of symmetry is x=9
the vertex represent a minimum