Question

PLEASE HELP ME!!!
Find the vertex of f(x)=x^2+2x+3 and show your work

Answer 1

The vertex is the point (-1,2)

Explanation:

we have

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

Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`f(x)-3=x^(2)+2x`

Complete the square. Remember to balance the equation by adding the same constants to each side.

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

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

Rewrite as perfect squares

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

`f(x)=(x+1)^(2)+2` ----> equation in vertex form

The vertex is the point (-1,2)