The function:
[tex]y=2x^2-12x+20[/tex]has the form:
[tex]y=ax^2+bx+c[/tex]with a = 2, b = -12, and c = 20.
The vertex form of a quadratic function is:
[tex]y=a(x-h)^2+k[/tex]where (h,k) is the vertex.
The x-coordinate of the vertex, h, is computed as follows:
[tex]\begin{gathered} h=\frac{-b}{2a} \\ h=\frac{-(-12)}{2\cdot2} \\ h=\frac{12}{4} \\ h=3 \end{gathered}[/tex]The y-coordinate of the vertex, k, is found replacing h into the formula of the function, as follows:
[tex]\begin{gathered} k=2h^2-12h+20 \\ k=2\cdot3^2-12\cdot3+20 \\ k=18-36+20 \\ k=2 \end{gathered}[/tex]Finally, the quadratic function in vertex form is:
[tex]y=2(x-3)^2+2[/tex]