Chapter 3 - Quadratic Functions - 3.2 The Vertex of a Parabola - Exercises and Problems for Section 3.2 - Exercises and Problems - Page 127: 4

Vertex: $(1,2)$ Axis of symmetry: $x=1$

To write the equation in vertex form we complete the square. $$ \begin{aligned} y & =3 x^2-6 x+5 \\ & =3\left(x^2-2 x\right)+5 \\ & =3\left(x^2-2 x+1\right)+5-3 \\ & =3(x-1)^2+2 \end{aligned} $$ The vertex is $(1,2)$ and the axis of symmetry is $x=1$.