Problem preview
F-IF.7.b Warmup M3-024-A08-V01

Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions.

Write an equation for a transformed absolute-value graph from its vertex and one other feature

Problem

Write the absolute-value equation with vertex \((2,~-3)\), opening upward, and arm slope magnitude \(4\).

Big Picture

What this problem is really about

Build the absolute-value rule from its geometric parts. The vertex supplies the two shifts, the upward opening fixes the coefficient’s sign, and the rise for a one-unit run gives its magnitude. Substituting one nearby point provides a fast check before writing the completed equation.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
F-IF.7.b
Category
Functions
Domain
Interpreting Functions
Objective
Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions.
Problem type
Write an equation for a transformed absolute-value graph from its vertex and one other feature