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Graphing absolute value functions worksheets
Graph eight absolute value functions or write equations from eight V-shaped graphs. Practice translations and reflections of y = |x| with integer vertices and a separate worked graphical key.
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In graph mode, plot the vertex and draw both branches from the supplied equation. In write-equation mode, read the vertex and opening direction of each V, then write its equation.
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Begin at the vertex and build two branches
For y = a|x − h| + k, the vertex is (h, k). A coefficient a = 1 opens the graph upward; a = −1 reflects it downward. Equal horizontal distances on either side of the vertex give equal y-values.
Each worksheet contains eight unique functions with integer vertices from −4 to 4 and unit-scaled axes from −5 to 5. Four open upward and four downward. Choose graph mode to draw from equations, or write-equation mode to recover a formula from each graph.
Questions about absolute value practice
What do the two modes ask students to do?
Graph mode supplies an equation and a blank coordinate grid. Write-equation mode supplies the V-shaped graph and an equation response line. Each worksheet has eight tasks and eight marks; the key completes the equation, vertex, opening direction and graph.
Which transformations are included?
Each set has four upward and four downward functions with a = 1 or −1. Integer vertex coordinates h and k range from −4 to 4. This activity focuses on translations and reflection; it does not include other stretch factors.
Does a branch end at the edge of the printed grid?
No. The grid shows the part of the function within −5 to 5 on each axis, with unit ticks. The branches continue beyond that viewing window. The vertex is where the two branches meet, not an endpoint of the whole function.
How do I recover the equation from the graph?
Read the vertex (h, k), choose a = 1 for an upward V or a = −1 for a downward V, then write y = a|x − h| + k. Check a second point on one branch and a matching point on the other.
Learning objective
What this activity builds
Connect the vertex and opening direction of an absolute value graph with y = a|x − h| + k.
Worked example
Graph y = −|x − 2| + 1 and describe its vertex.
The vertex is (2, 1). The graph opens downward and passes through (1, 0), (3, 0), (0, −1) and (4, −1).
At x = 2 the absolute value is zero, giving y = 1. Moving one unit to either side makes the absolute value one, so the negative coefficient lowers y by one. Both branches begin at the vertex; they do not continue through it as crossing lines.
Teaching notes
Make the practice count
- Find the vertex before plotting other points.
- Read x − h as a horizontal translation: x + 3 means h = −3.
- Use matching distances left and right of the vertex to check symmetry.
- Use the sign of a to distinguish upward and downward openings.
- In write-equation mode, substitute a visible point to check the sign and translation.
Make it yours
Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose graphing or equation-writing practice. Each set has eight functions with upward and downward graphs. Every grid uses unit intervals from −5 to 5.
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