On graph paper, sketch the parabola that is the set of all points equidistant from the focus $\left(0, −5\right)$ and the directrix $y = 7$.

1. Find and simplify the equation of the parabola.

   Answer (a):

   Now simplify.

2. Change the equation of the parabola to shift the graph up $3$ units. What would the vertex of the new parabola be?

   Hint (b):

   What operation do you perform on the equation to shift the graph up $3$units?

3. What would the new focus point be, and what line would be the new directrix?

   Hint (c):

   When the graph is shifted up 3 units, what happens to the focus and directrix?