Chapter 3 - Quadratic Functions - 3.1 Introduction to the Family of Quadratic Functions - Exercises and Problems for Section 3.1 - Exercises and Problems - Page 121: 34

See the graph

Factoring gives $y=3 x^2-16 x-12=(3 x+2)(x-6)$. The zeros are $x=-\frac{2}{3}$ and $x=6$, the axis of symmetry is halfway between the zeros, $x=\frac{-\frac{2}{3}+6}{2}=\frac{8}{3}$. The $y$ value of the vertex is $$ y=3\left(\frac{8}{3}\right)^2-16\left(\frac{8}{3}\right)-12=-\frac{100}{3} $$ See the graph.