A parabola has its vertex at (2, 2), and the equation of its directrix is y = 2.5. The equation that represents the parabola is

We are given with

vertex coordinates: (2, 2)

equation of directrix: y = 2.5

The distance between the focus and the vertex is

2.5 - 2.0 = 0.5

The focus then is at

(2.0 - 0.5, 2.0) = (1.5, 2.0)

The equation of the parabola is

(y - 2) = 4 (0.5) (x - 2) ^2

y = 2 (x - 2) ^2 + 2

y = 2x^2 - 8x + 10