On your paper, sketch a parabola with focus $(1, -2)$ and directrix $y = -4$.

1. Where is the vertex of the parabola?

   Hint (a):

   The vertex is halfway between the focus and the directrix.

2. Write an expression for the distance from the focus to any point $(x, y)$ on the parabola.

   Answer (b):

   $\sqrt{(x-1)^2+(y+2)^2}$ 

3. Write an expression for the distance from the directrix to any point $(x, y)$ on the parabola.

   Answer (c):

   $y + 4$ 

4. If all of the points on a parabola are equidistant from the focus and the directrix, use your expressions from parts (b) and (c) to write an equation for the parabola in graphing form. How can you check your equation?

   Answer (d):

   $y=\frac{1}{4}(x-1)^2-3$ 

   The vertex matches the answer from part (a). Check another point on the parabola to confirm that it is equidistant from the focus and directrix, such as $(-1, -2)$.