Analyze graph transformations caused by f(x)+k, kf(x), f(kx), and f(x+k); identify even/odd functions.
Match a transformed equation to a graph description
Problem
Relative to \(y=x^{2}\), analyze \(y=(x-3)^{2}+2\).
Big Picture
What this problem is really about
Start from the parent parabola’s vertex and opening direction, then read the equation by where each change occurs. The expression inside the square controls horizontal placement, the term outside controls vertical placement, and the leading coefficient controls reflection and width. Those features together give a complete graph description without plotting every point.
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