Answer:
[tex]P(1,5)[/tex]
Explanation: Axis of symmetry is a vertical line that makes function symmetrical along either side:
In case of parabla function or:
[tex]y(x)=3x^2-6x+8[/tex]We get axial symmetry where the first derivate is zero, and in fact, that is the x value for vertex:
Therefore:
[tex]\begin{gathered} f^{\prime}(x)=(3x^2-6x+8)^{\prime}=6x-6=0 \\ \therefore\rightarrow \\ x=\frac{6}{6}=1 \end{gathered}[/tex]And the corresponding y-value is:
[tex]f(1)=3(1)^2-6(1)+8=5[/tex]Therefore vertex is at the point:
[tex]P(1,5)[/tex]