ANSWER
[tex]y = 2{(x - 1)}^{2} + 3[/tex]
EXPLANATION
The vertex of the given parabola is;
[tex](h,k)=(1,3)[/tex]
and the focus is
[tex](1,3.5)[/tex]
The given parabola has the line of symmetry parallel to the y-axis.
It's equation is given by;
[tex](y - k) = 4p {(x - h)}^{2} [/tex]
[tex] |p| = 0.5[/tex]
The distance from the focus to the vertex.
[tex]p = 0.5[/tex]
The parabola will open up because the directrix is
[tex]y = 2.5[/tex]
The equation of the parabola is
[tex](y - 3) = 4 \times 0.5{(x - 1)}^{2} [/tex]
Or
[tex]y = 2{(x - 1)}^{2} + 3[/tex]
