SOLUTION: The coordinates of the focus and equation of the directrix of a parabola are given. Write an equation for each parabola. Then draw the graph 35. (-3, -2);y=-6

We'll draw the graph first.  Draw the focus and the directrix:



Draw a line segment from the focus directly to the directrix:

 

The vertex is the point halfway between the focus and the
directrix.  That is the midpoint of the line segment we just
drew.  We can tell this is (-3,-4), so that is the vertex.
(h,k) = (-3,-4). Let's plot the vertex:



The distance from the vertex to the focus is called p,
This is 2 units.  And it is upward from the vertex to the
focus, so it is +2. (If it had been downward we would have
made it negative.)  So p = 2.

Now draw a square with that line segment as its left
side: 



Now draw another square with that line segment as its right
side:




Now use the outer upper corners of the squares and the
vertex to sketch the parabola:




Now we can erase all the guide lines and just leave the
parabola, the vertex, the focus and the directrix:




Now we have found the vertex (h,k) = (-3,-4), and
the focal length p = 2 from the vertex to the focus.

The equation of a U-shaped parabola is

(x - h)² = 4p(y - k)

So we substitute -3 for h, -4 for k and 2 for p


(x - (-3) )² = 4(2)(y - (-4) )

    (x + 3)² = 8(y + 4)

That's it!

Edwin