ANSWER
(-1,2)
EXPLANATION
The given quadratic expression is:
[tex]f(x) = {x}^{2} + 2x + 3[/tex]
The coefficient of the quadratic term is already 1.
So we add and subtract the square of half the coefficient of x.
[tex]f(x) = {x}^{2} + 2x + 1 - 1+ 3[/tex]
We factor the first three terms to obtain
[tex]f(x) =(x + 1)^{2} + 2[/tex]
This is now in the form:
[tex]f(x) = a({x - h)}^{2} +k[/tex]
where (h,k) which is equal to (-1,2) is the vertex.
