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F-BF.3 Warmup M2-016-A07-V04

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

Write the absolute-value function indicated by vertex \((2,-3)\), downward opening, and arm-slope magnitude \(0.5\). Determine the signed coefficient in \(f(x)=a|x-2|-3\) and check the vertex and values at \(x=1\) and \(x=3\).

Absolute-value feature-givens plot marking vertex (2, −3), opening downward, with run 1 and change −0.5 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