Question

The vertex of a parabola is (-3,1) and it’s directrix y=6 write the quadratic function of the parabola

Answer 1

This parab. is a vertical one, opening down.  
The standard equation of a parabola appying here is 4p(y-k) = (x-h)^2.
Take the values of h and k from the given vertex and subst. them into this equation:

4p(y-1) = (x+3)^2

Now p is the distance between vertex and directrix; that distance is 5 units (which is 6 less 1).  Thus, the equation of the parabola becomes

4(5)(y-1) = (x+3)^2, or y-1 = (1/20)(x+3)^2    (answer)