Question

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

Answer 1

Answer:

The vertex is the point (-1,2)

Step-by-step 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)