Answer:
[tex]f(x)=(x+3)^{2}-6[/tex]
Step-by-step explanation:
we have
[tex]f(x)=x^{2} +6x+3[/tex]
we know that
The equation of a vertical parabola into vertex form is equal to
[tex]f(x)=a(x-h)^{2}+k[/tex]
where
(h,k) ------> is the vertex of the parabola
Convert the function 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} +6x[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]f(x)-3+9=x^{2} +6x+9[/tex]
[tex]f(x)+6=x^{2} +6x+9[/tex]
Rewrite as perfect squares
[tex]f(x)+6=(x+3)^{2}[/tex]
[tex]f(x)=(x+3)^{2}-6[/tex] -----> function in vertex form
