Answer:
[tex]2(x-1)^{2}=4[/tex]
Step-by-step explanation:
we have
[tex]2x^{2} -4x-2=0[/tex]
This is the equation of a vertical parabola open upward
The vertex is a minimum
Convert the equation into vertex form
Group terms that contain the same variable and move the constant to the other side
[tex]2x^{2} -4x=2[/tex]
Factor the leading coefficient
[tex]2(x^{2} -2x)=2[/tex]
[tex]2(x^{2} -2x+1)=2+2[/tex]
[tex]2(x^{2} -2x+1)=4[/tex]
Rewrite as perfect squares
[tex]2(x-1)^{2}=4[/tex] -----> this is the answer
The vertex is the point (1,-4)
