Write the equation of a function in graphing form for each parabola described below.  

1. A parabola with vertex ($0, -5$) that passes through the point ($-1, 2$).

   Hint (a):

   Use the equation $f(x) = a(x - h)^2 + k$, where ($h, k$) is the vertex.

   Step 1(a):

   $f(x) = a(x - 0)^2 - 5$

   Step 2(a):

   Use the point ($-1, 2$) to solve for $a$.
   $2 = a(-1 - 0)^2 - 5$

   Answer (a):

   $f(x) = 7x^2 - 5$

2. A parabola with vertex ($1, 4$) that passes through the point ($5, -4$).

   Hint (b):

   Follow the same steps detailed in part (a).