Given the quadratic equation expressed as:
[tex]f(x)=3x^2-4x[/tex]Factor out 3 from the expression
[tex]f(x)=3(x^2-\frac{4}{3}x)[/tex]Complete the square of the expression in bracket
[tex]\begin{gathered} f(x)=3(x^2-\frac{4}{3}x+(\frac{1}{2}\cdot\frac{4}{3})^2-(\frac{1}{2}\cdot\frac{4}{3})^2) \\ f(x)=3(x^2-\frac{4}{3}x+(\frac{2}{3})^2-(\frac{2}{3})^2) \\ f(x)=3(x^2-\frac{4}{3}x+(\frac{2}{3})^2-\frac{4}{9}) \\ f(x)=3(x-\frac{2}{3})^2-3(\frac{4}{9}) \\ f(x)=3(x-\frac{2}{3})^2-\frac{4}{3} \\ \end{gathered}[/tex]Since the vertex form of a quadratic equation is in the form f(x) = a(x-h)^2+k where (h, k) is the vertex.The vertex of the resulting function is (2/3, -4/3)