Problem preview

F-IF.7.b Warmup M2-022-A09-V03

Graph square-root, cube-root, absolute-value, step, and piecewise-defined functions, showing key features by hand in simple cases and with technology when the functions are more complicated.

Write an absolute-value equation from a vertex, opening direction, and arm slope

Problem

Write the absolute-value equation for the graph with vertex \((0,1)\), upward opening, and arm slope magnitude \(0.5\). Start with \(y=a|x-h|+k\), determine \(a\), \(h\), and \(k\) from the features, and verify a point \(\text{two}~\text{units}\) from the vertex on the graph scaffold.

Source absolute-value graph with vertex (0,1), opening upward, and arm slope magnitude 0.5.

Answer choices

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Preview only

y=-0.5|x|+1

y=0.5|x|+1

y=0.5|x+1|

y=|x|+1

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Curriculum context

Course: Math II
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 absolute-value equation from a vertex, opening direction, and arm slope