Question

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

Answer 1

ANSWER

(-1,2)

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.