Question

Which function in vertex form is equivalent to f(x) = x2 + x +1?

Answer 1

Explanation:

Given is a function in vertex form

`f(x) = x^2+x+1\\`

Complete the squares to get in square form

`x^2+2(x)((1)/(2) )+(1)/(4) +(3)/(4) \\(x+(1)/(2) )^2+(3)/(4)`

This is in vertex form

Vertex is (-1/2,3/4)

Answer 2

f(x) = x^2 + x + 1
f(x) = x^2 + x + 1/4 + 1 - 1/4
f(x) = (x + 1/2)^2 + 3/4