Question

Express the function y = 2x^2 + 8x + 1 in vertex form.

Answer 1

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 $y=2(x+2)^2-7.$

Answer 2

Your answer in Vertex Form :
y = 2(x+2)^2-7