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F-BF.3 Warmup M2-016-A07-V02

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

Use the plot's vertex \((-4,1)\), downward opening, and arm-slope magnitude \(2\) to construct an absolute-value function. Explain the sign and magnitude of \(a\) in \(f(x)=a|x+4|+1\), then verify the vertex and values \(\text{one}~\text{unit}\) to either side.

Absolute-value feature-givens plot marking vertex (−4, 1), opening downward, with run 1 and change −2 on an arm; no completed graph or equation is shown. Open full size
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Four variants of this problem type
Curriculum context
Course
Math II
Standard
F-BF.3
Category
Functions
Domain
Building Functions
Objective
Analyze transformations of quadratic and absolute-value functions and identify even/odd functions.
Problem type
Write an absolute-value function from its vertex, opening direction, and arm steepness