A parabola has its vertex at (2, 2), and the equation of its directrix is y = 2.5 what is the parabola

Question

I need help fast

Answer 1

Since the vertex is below the directrix, this is a downward opening parabola.  

The P value, the distance between the vertex and the directrix,   is 2.5 - 2 = 0.5  .    

The relation between the P value and a, the magnitude of the coefficient of the quadratic term, is 

   a =  1( 4 P)  ,  so  the magnitude of a is  1/2.   Since this is a downward opening parabola, 

this means that   a =  - 1/2.

 

 The  general vertex equation for a parabola is: 

  y =  a (x -x_v)² + b

Since the vertex is located at (2,2),   x_v  = 2   and b =2

 

Putting this together results in:

 

  y = -(1/2) (x -2)²  +2