SOLUTION: Can you write the equation of a parabola when given only the coordinates of the vertex

No.  The equation of a parabola is 

f(x) = a(x - h)² + k

where (h,k) = the vertex.  However, the smaller the value of |a|,
the wider the parabola and the larger the value of |a|, the narrower.
When "a" is a positive number, the parabola opens upward. When "a" 
is negative the parabola opens downward.   

Here are five different parabolas, all with the same vertex 
(h,k) = (3,-2) but with different values of "a".



Edwin