Algebra-2

Question Analysis
This question involves identifying the parent function from which the given transformed function is derived.
The main focus is on recognizing the base form of the quadratic function family, which undergoes a horizontal shift transformation.

Key Concept Explanation
Parent functions are the simplest forms of a function family. For quadratic functions, the parent function is , which has a parabola graph with its vertex at the origin (0, 0).
Transformations like horizontal shifts modify the parent function, but the core form (squared term) remains, indicating it belongs to the quadratic family with as the parent.

Step-by-Step Solution
Observe the given function: .
Notice that the function involves a squared variable term, which is characteristic of quadratic functions.
Recall that the simplest quadratic function (parent function) is

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