Analyze transformations of quadratic and absolute-value functions and identify even/odd functions.
Write an absolute-value function from its vertex, opening direction, and arm steepness
Problem
From the feature plot, write an absolute-value function with vertex \((3,2)\), upward opening, and arm-slope magnitude \(1\). Determine \(a\) in \(f(x)=a|x-3|+2\) and verify the vertex and \(\text{one}~\text{symmetric}~\text{pair}\) of points.
The vertex determines the horizontal and vertical shifts in absolute-value form, while the arm information determines the remaining coefficient. We’ll use the arm-slope magnitude for the coefficient’s magnitude, the upward opening for its sign, and symmetric equal-offset inputs to verify the fitted V.
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