SOLUTION: What is the equation of a parabola with vertex (0,0) and focus (0,4)? Draw its graph on the grid

Let's draw it first:

Plot the vertex and the focus:



Draw another point just as far below the vertex as the focus
is above the vertex.  Since the focus is 4 units above
the vertex, we will draw a point 4 units below the vertex,
at (0,-4)



Now draw a square on the RIGHT with that whole line as a side:



Now draw a square on the LEFT with that same whole line as a side:



Now sketch the parabola with vertex at (0,0) which goes
through the upper corners of those squares.



The directed diatance from the vertex to the focus is called
p, the "parabolic constant".  If going from vertex to focus is 
an upward or rightward motion, then p is positive.  If downward 
or leftward, then p is negative.  Here p is positive, in fact,
it is +4 because going from the vertex (0,0) to the focus is

The equation of a parabola with vertex at the origin where going
from vertex to focus is vertical is



(If that motion had been horizontal, x and y would be switched)

 So since p = +4, that becomes:





[Incidentally the line which the bottom side of those
two squares are part of is called the directrix.  It's
equation is y = -4.]

Edwin