Answer:
Vertex: (4,-1)
Explanation:
Given the quadratic function:
[tex]y=2x^2-16x+31[/tex]Comparing it with the quadratic function: y=ax²+bx+c
[tex]a=2,b=-16,c=31[/tex]First, determine the x-value of the vertex using the formula: x=-b/2a
[tex]\begin{gathered} x=-\frac{b}{2a} \\ =-\frac{-16}{2\times2} \\ =\frac{16}{4} \\ x=4 \end{gathered}[/tex]Next, substitute x=4 into y.
[tex]\begin{gathered} y=2x^2-16x+31 \\ =2(4^2)-16(4)+31 \\ =2(16)-64+31 \\ =32-64+31 \\ y=-1 \end{gathered}[/tex]Therefore, the vertex of the function will be:
[tex](4,-1)[/tex]