SOLUTION: What is the equation of a parabola with the vertex (3,2) and focus (4,2)?

The equation of a parabola is

(x-h)² = 4p(y-k) if the vertex and focus are above or below
one another. p is positive if the vertex is below the focus
and negative if the vertex is above the focus.

(y-k)² = 4p(x-h) if the vertex and focus are right or left
of each other. p is positive if the vertex is left of the focus
and negative if the vertex is to the right the focus. 

where 

h = the x-coordinate of the vertex = 3
k = the y-coordinate of the vertex = 2
p = the distance from the vertex to the focus.

The vertex (3,2) is left of the focus (4,2) so 
 
The distance between the vertex (3,2) and focus (4,2)
is 1 unit, and the vertex is left of the focus,
so p = +1

Plug in the numbers for h, k, and p and leave x and y
as letters, and you'll have the desired equation.

Here's the graph.  The blue line is the line of symmetry.
It goes through both the vertex and the focus.

The green line is the directrix which is |p|
units from the vertex, outside the parabola, and is
perpendicular to the line of symmetry:



Edwin