Analyze transformations of quadratic and absolute-value functions and identify even/odd functions.
Interpret \(f(x)+k\) as a vertical shift of a quadratic or absolute-value function
Problem
Identify the vertical shift from parent function \(f(x)=x^2\) to transformed function \(g(x)=x^2+5\).
Big Picture
What this problem is really about
A constant added outside the function changes every output while leaving each input fixed. We’ll express the transformed rule as the parent output plus a constant, use its sign for the vertical direction, and track the parent vertex to verify the shift without changing shape or symmetry.
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