f(x) = 2(x + 1)² - 2
Explanation:The given function is:
[tex]f(x)=2x^2+4x[/tex]Factor 2 out of the expression
[tex]f(x)=2(x^2+2x)[/tex]Use the completing the square rule
[tex]\begin{gathered} f(x)=2(x^2+2x+1^2-1^2) \\ f(x)=2\lbrack(x+1)^2-1\rbrack \end{gathered}[/tex]Expand the expression
[tex]f(x)=2(x+1)^2-2[/tex]Therefore, the vertex form of f(x) = 2x² + 4x is:
f(x) = 2(x + 1)² - 2
