Respuesta :
Answer:
[tex]f(x)=(x+3)^2-6[/tex]
Step-by-step explanation:
We have been given a function [tex]f(x)=x^2+6x+3[/tex]. We are asked to find the function equivalent to our given function in vertex form.
To convert our given function in vertex form, we need to complete the square for our given function as:
Add and subtract [tex](\frac{b}{2})^2[/tex] from equation:
[tex](\frac{b}{2})^2=(\frac{6}{2})^=3^2=9[/tex]
[tex]f(x)=(x^2+6x+9)+3-9[/tex]
[tex]f(x)=(x^2+2\cdot 3x+3^2)-6[/tex]
[tex]f(x)=(x+3)^2-6[/tex]
Therefore, the [tex]f(x)=(x+3)^2-6[/tex] is equivalent to our given function in vertex form.
