Recall what you know about translations of functions.

1. What is the equation of the parabola that is identical in shape to $f(x) = x^2$, but has its vertex at $(5, 2)$?

   Hint (a):

   Recall that vertex form for a parabola is $y = a(x - h)^2 + k$.

2. Write an equation of a cosine curve that has a maximum at $(2, –1)$.

   Hint (b):

   The function $f(x) = \cos(x)$ has a maximum point at $(0, 1)$.
   How far does the original function need to be translated horizontally? Vertically?