Question

PLEASE HELP
find the vertex of f(x)=x^2+2x+3 (make sure you show your work)

Answer 1

(-1,2)

Step-by-step explanation

The given quadratic expression is:

`f(x) = {x}^(2) + 2x + 3`

The coefficient of the quadratic term is already 1.

So we add and subtract the square of half the coefficient of x.

`f(x) = {x}^(2) + 2x + 1 - 1+ 3`

We factor the first three terms to obtain

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

This is now in the form:

`f(x) = a({x - h)}^(2) +k`

where (h,k) which is equal to (-1,2) is the vertex.