Recall what you know about the translation 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. Find an equation of a cosine curve that has a maximum at $(2, −1)$.

   Hint (b):

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