Answer:
[tex]\displaystyle f(x)=\frac{1}{2}x^2-2x-2[/tex]
Step-by-step explanation:
To convert from vertex form to standard form, we can simply expand.
So, we have:
[tex]\displaystyle f(x)=\frac{1}{2}(x-2)^2-4[/tex]
Expand the square:
[tex]\displaystyle f(x)=\frac{1}{2}(x^2-4x+4)-4[/tex]
Distribute:
[tex]\displaystyle f(x)=\frac{1}{2}x^2-2x+2-4[/tex]
Simplify:
[tex]\displaystyle f(x)=\frac{1}{2}x^2-2x-2[/tex]
