Answer :
For the function given as;
[tex]f(x)=5x^2-6x+12[/tex]The axis of symmetry is the straight line that divides the parabola into 2 equal halves.
[tex]\begin{gathered} The\text{ x vertex is given as;} \\ x_{\text{vertex}}=-\frac{b}{2a} \\ In\text{ the equation,} \\ 5x^2-6x+12 \\ a=5,b=-6,c=12 \\ x_{\text{vertex}}=-\frac{-6}{2(5)} \\ x_{\text{vertex}}=\frac{6}{10} \\ x_{\text{vertex}}=\frac{3}{5}\text{ (thats }\frac{6}{10}\text{ in its simplest form)} \end{gathered}[/tex]