Answer: [tex]y=(x +3)^2 -6[/tex]
Step-by-step explanation:
The equation of a parabola in Vertex form is:
[tex]y=a(x-h)^2+k[/tex]
Where [tex](h,k)[/tex] is the vertex of the parabola
We can rewrite the function [tex]f(x)= x^2 + 6x + 3[/tex] as:
[tex]y= x^2 + 6x + 3[/tex]
In order to convert it into vertex form we need to Complete the square:
Take the coefficient of the x term, divide it by 2 and square it:
[tex](\frac{6}{2})=3^2[/tex]
Add and subtract 3² on the right side:
[tex]y= x^2 + 6x+3^2 + 3-3^2[/tex]
Now we must convert the right side to a squared expression, then we get:
[tex]y=(x +3)^2 -6[/tex]
