ANSWER
[tex]y ={x}^{2} + 2[/tex]
EXPLANATION
The equation of a parabola that has vertex at (h,k) is given by:
[tex]y = a {(x - h)}^{2} + k[/tex]
If the given parabola has vertex at (0,2), then h=0 and k=2.
Considering the possible answers, we must have a=1.
We substitute the values in to the formula to get:
[tex]y =1 {(x - 0)}^{2} + 2[/tex]
[tex]y ={x }^{2} + 2[/tex]
The first option is correct.
