Answer: The vertex form of the given function is [tex]y=2(x+2)^2-7.[/tex]
Step-by-step explanation: We are given to express the following function in vertex form.
[tex]y=2x^2+8x+1~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that the vertex form of a quadratic function [tex] y=ax^2+bx+c[/tex] is given by
[tex]y=a(x - h)2+k,[/tex] where (h, k) is the vertex.
From equation (i), we have
[tex]y=2x^2+8x+1\\\\\Rightarrow y=2(x^2+4x+4)-8+1\\\\\Rightarrow y=2(x+2)^2-7.[/tex]
Thus, the vertex form of the given function is [tex]y=2(x+2)^2-7.[/tex]
