Which of the following describes the vertical translation applied to the function $y=(x+1{)}^2$ to obtain the graph of $y=x^2+2x+5$?

True or False: If $f(x)$ is a linear function with equation $y=mx+c$ (where $m\ne 0$), then for any vertical translation $k\ne 0$, the graph of $g(x)=f(x)+k$ will be parallel to and never intersect the graph of $f(x)$.

If the graph of $$y=f(x)$$ is translated vertically by $$k$$ units such that the resulting graph is identical to the original graph (i.e., $$f(x)+k=f(x)$$ for all $$x$$), what must be the value of $$k$$?

The quadratic function $f(x)=x^2-4x+1$ is translated vertically upwards by $2$ units to form the function $g(x)$. What are the coordinates of the vertex of the graph of $g(x)$?

True or False: Based on the vertex form $y=a(x-h{)}^2+k$, the value of $k$ directly represents the vertical translation of the parent function $y=a{x}^2$.