Answer:
The vertex is the point (-1,2)
Step-by-step explanation:
we have
[tex]f(x)=x^{2}+2x+3[/tex]
Convert into vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)-3=x^{2}+2x[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side.
[tex]f(x)-3+1=x^{2}+2x+1[/tex]
[tex]f(x)-2=x^{2}+2x+1[/tex]
Rewrite as perfect squares
[tex]f(x)-2=(x+1)^{2}[/tex]
[tex]f(x)=(x+1)^{2}+2[/tex] ----> equation in vertex form
The vertex is the point (-1,2)
