The equation of a parabola with vertex (h,k) is given by:
[tex]y=a(x-h)^2+k[/tex]Starting from the given equation, complete the square to write the function in vertex form:
[tex]\begin{gathered} f(x)=4x^2-8x+6 \\ =4(x^2-2x)+6 \\ =4(x^2-2x+1-1)+6 \\ =4(x^2-2x+1)+4(-1)+6 \\ =4(x-1)^2-4+6 \\ =4(x-1)^2+2 \end{gathered}[/tex]By comparing that equation with the vertex form of a parabola, we can see that h=1 and k=2.
Therefore, the vertex of the given quadratic polynomial, is:
[tex](1,2)[/tex]