After translation of the graph 4unit right and 1unit down the function of the graph [tex]h(x) = (x+4)^{2} -1[/tex].
What is translation?
" Translation is defined as the displacement of the geometrical shape as per the given condition in the coordinate plane."
According to the question,
Given function,
[tex]f(x) = x^{2}[/tex]
As per the given condition,
Graph of h is a translation 4 units right and 1 unit down of the graph of f(x).
x translated by 4 unit right[tex]= ( x + 4) ^{2}[/tex]
f(x) translated 1 unit down[tex]= f(x) -1[/tex]
Vertex form of function [tex]h(x) = ( x + 4) ^{2} -1[/tex]
Hence, Option(A) is the correct answer.
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