Worksheets · Algebra 1

Graphing absolute value equations worksheet

An absolute value graph is two straight pieces meeting at a point. Find the vertex, then the slope tells you how steep each arm is.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Absolute Value

Date Period

Graph each equation.

  1. Graph y=− ⁣∣x+3∣−10−10−5−5551010
  2. Graph y=−2 ⁣∣x−5∣−3−10−10−5−5551010
  3. Graph y=3 ⁣∣x+1∣−10−10−5−5551010
  4. Graph y=∣x+1∣−2−10−10−5−5551010
  5. Graph y=∣x∣−6−10−10−5−5551010
  6. Graph y=− ⁣∣x−4∣−4−10−10−5−5551010
  7. Graph y=∣x−2∣−3−10−10−5−5551010
  8. Graph y=− ⁣∣x+1∣−3−10−10−5−5551010
  9. Graph y=∣x−3∣+1−10−10−5−5551010
  10. Graph y=− ⁣∣x−1∣+4−10−10−5−5551010
  11. Graph y=−2 ⁣∣x∣+6−10−10−5−5551010
  12. Graph y=3 ⁣∣x+6∣+8−10−10−5−5551010
  13. Graph y=∣x+1∣+1−10−10−5−5551010
  14. Graph y=− ⁣∣x+4∣+2−10−10−5−5551010
  15. Graph y=2 ⁣∣x∣−5−10−10−5−5551010
  16. Graph y=∣x−3∣−10−10−5−5551010
  17. Graph y=−2 ⁣∣x+5∣−4−10−10−5−5551010
  18. Graph y=−2 ⁣∣x+7∣+7−10−10−5−5551010
  19. Graph y=− ⁣∣x∣+1−10−10−5−5551010
  20. Graph y=−2 ⁣∣x−2∣+2−10−10−5−5551010

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Absolute ValueAnswer keyVersion 1

Date Period

Graph each equation.

  1. Graph y=− ⁣∣x+3∣−10−10−5−5551010vertex (−3,0), opens down
  2. Graph y=−2 ⁣∣x−5∣−3−10−10−5−5551010vertex (5,−3), opens down
  3. Graph y=3 ⁣∣x+1∣−10−10−5−5551010vertex (−1,0), opens up
  4. Graph y=∣x+1∣−2−10−10−5−5551010vertex (−1,−2), opens up
  5. Graph y=∣x∣−6−10−1051010−5−55vertex (0,−6), opens up
  6. Graph y=− ⁣∣x−4∣−4−10−5−5551010−10vertex (4,−4), opens down
  7. Graph y=∣x−2∣−3−10−10−5−5551010vertex (2,−3), opens up
  8. Graph y=− ⁣∣x+1∣−3−10−10−5−5551010vertex (−1,−3), opens down
  9. Graph y=∣x−3∣+1−10−10−5−5510105vertex (3,1), opens up
  10. Graph y=− ⁣∣x−1∣+4−10−10−5−5551010vertex (1,4), opens down
  11. Graph y=−2 ⁣∣x∣+6−10−10−5−5510105vertex (0,6), opens down
  12. Graph y=3 ⁣∣x+6∣+8−10−10−5−5551010vertex (−6,8), opens up
  13. Graph y=∣x+1∣+1−10−10−5−5551010vertex (−1,1), opens up
  14. Graph y=− ⁣∣x+4∣+2−10−10−5−5551010vertex (−4,2), opens down
  15. Graph y=2 ⁣∣x∣−5−10−10−5551010vertex (0,−5), opens up
  16. Graph y=∣x−3∣−10−10−5−5551010vertex (3,0), opens up
  17. Graph y=−2 ⁣∣x+5∣−4−10−10−5−5551010vertex (−5,−4), opens down
  18. Graph y=−2 ⁣∣x+7∣+7−10−10−5551010−5vertex (−7,7), opens down
  19. Graph y=− ⁣∣x∣+1−10−10−5−5551010vertex (0,1), opens down
  20. Graph y=−2 ⁣∣x−2∣+2−10−10−5551010−5vertex (2,2), opens down

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Graph y=∣x+1∣−2

  1. The vertex is at (-1, -2).
  2. The coefficient is 1, so each arm has slope 1 and -1.

The answer is vertex (−1,−2), opens up.

Where students go wrong

Drawing a curve instead of two straight arms. It is not a parabola: the pieces are straight lines, and they meet at a sharp point rather than rounding off.

Also called graphing absolute value functions or V shaped graphs.

Questions about these worksheets

Yes. Every graphing absolute value equations sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the graphing absolute value equations questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Drawing a curve instead of two straight arms. It is not a parabola: the pieces are straight lines, and they meet at a sharp point rather than rounding off.