We are given the following function that represents a parabola:
[tex]f(x)=3x^2-24x-9[/tex]
To determine the minimum value we will determine the vertex of the parabola. To do that we will convert the function into the following form:
[tex]f(x)=a(x-h)^2+k[/tex]
It has already been established that the vertex is:
[tex](h,k)=(4,-57)[/tex]
This means that the minimum value is at the points:
[tex]\begin{gathered} x=4 \\ y=-57 \end{gathered}[/tex]
Therefore, the minimum occurs at x = 4.
