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