Set up your worksheet
Start with a difficulty level, then change anything you like. Editing a setting moves the level over to Custom, and your other choices stay where they are.
Your worksheet
Version AA transformations worksheet you set up yourself
A lot of the transformation practice online arrives as a fixed PDF: twenty problems, one flavor, take it or leave it. That is fine on the day it happens to match your lesson. It is less useful on Tuesday, when part of the class is still reading a shift left as a plus sign and the rest are ready for a compression by two thirds.
This generator hands the choices back to you. You decide whether the parabolas move left, right or both. You decide whether |a| is 1, a whole number, a fraction, or a mix, and the reflection setting decides the sign separately. You decide whether students describe the transformations in words, build the equation from a description, name the vertex, name the axis, sketch the graph, or match a graph to its equation. Then you generate the sheet and the matching answer key.
The Version B button keeps every setting and swaps in fresh numbers, so two students sitting next to each other can work at the same level without copying the same answers. It works for retakes and make-up work as well.
What you can set
- Horizontal shifts — left only, right only, mixed, or none, with your own range for how far.
- Vertical shifts — up only, down only, mixed, or none, again with a range you set.
- Reflection — include a < 0, exclude it, or make every problem a reflection. When it is included you can also set roughly what share of the problems flip.
- Stretch and compression — no stretch or compression (|a| = 1), integer |a|, fractional |a|, or a mix of all three. The largest integer value of |a| is yours to cap. The sign of a comes from the Reflection control, so these settings stay independent.
- Zero shifts — a checkbox mixes a few problems with h = 0 or k = 0 into the page, so students meet a parabola that only moves one direction.
- Student task — check any combination of identify transformations, write vertex form, identify the vertex, identify the axis of symmetry, graph the quadratic, and match graph to equation. Checking several rotates through them across the page.
- Page setup — problem count, work space size, one or two columns, grid range for the graphs, your own title, and your own footer credit.
How to make a quadratic transformations worksheet
- Pick a difficulty level as a starting point, or go straight to Custom.
- Set the shifts, the reflection rule and the stretch factor to match what you taught.
- Check the student tasks you want on the page.
- Choose a problem count and how much work space each problem gets.
- Press Generate new worksheet, then print it or download the PDF or Word file.
- Press Create Version B if you want a second set with the same settings.
The three difficulty levels
The levels are presets, not locked settings. Load one, then change whatever you want.
| Level | What it produces | Sample problem |
|---|---|---|
| Level 1 — Basic | a = 1, shifts from 1 to 6, no reflections. Students name the vertex, the axis, and the shifts. Good for the first day in vertex form. | y = (x − 4)² + 3 |
| Level 2 — Standard | Integer values of a up to 4, shifts from 1 to 9, reflections mixed in. Students describe all four transformations and write vertex form from a description. | y = −2(x + 3)² + 5 |
| Level 3 — Advanced | Integer and fractional values of a, shifts up to 12, reflections mixed in, and all six task types in rotation, including graphing and graph matching. | y = 23(x + 7)² − 11 |
What students write down
Take y = −2(x + 3)² + 5. A full answer on an identify-transformations problem reads: left 3, up 5, reflected over the x-axis, vertical stretch by 2, vertex (−3, 5), axis of symmetry x = −3. The answer key spells out each piece the same way, so a student checking their own work can see which part slipped rather than just a red mark on the whole problem.
The sign of h is where a lot of the confusion lives. Vertex form subtracts h, so (x + 3)² carries h = −3 and moves the parabola left. If your class is working on that specifically, set horizontal shifts to Left only for a page, then switch to Mixed once it settles.
Looking for more practice? Browse our free quadratic worksheets for graphing, vertex form, factoring, solving, and other quadratic topics.
Questions teachers ask
Is this free?
Yes. There is no account, no sign-up and no watermark, and the worksheets you make here are yours to print, copy and use with your students.
Can I save it as a PDF?
Press Download PDF and your browser's print dialog opens with the worksheet laid out. Choose "Save as PDF" as the destination. Print answer key does the same thing for the key.
Can I edit the worksheet in Word?
Download Word gives you a .doc file that opens in Word, Google Docs and LibreOffice, and the text is editable once it is open. Graph grids are drawn as vector images and some versions of Word handle them poorly, so for graphing and matching pages the PDF usually looks closer to what you see on screen.
Will the vertex stay on the grid for graphing problems?
Graphing and matching problems pull their vertex from inside the grid range you chose, so the turning point lands on the paper. The arms of a steep parabola still run off the top of the grid, which is normal and usually worth a sentence in class.
Why did the matching problems disappear?
A matching problem needs four different quadratics to sit under four different graphs. Some combinations describe fewer than four — turning off both shifts with |a| = 1 leaves only y = x², for instance. When that happens the page says so and fills those slots with your other selected tasks. Widening a shift range, allowing reflections, or adding a second stretch factor brings matching back.
Can I use fractional stretch factors?
Set Stretch / compression to Fractional |a| for halves, thirds and quarters, or to Mixed if you want fractions and whole numbers on the same page. Fractions with a value under 1 are described as a vertical compression in the answer key, and those over 1 as a stretch.
How do I make a second version for a make-up test?
Press Create Version B. Every setting stays put and the numbers change. The version label at the top of the sheet updates so you can tell the two apart after they are printed.
What grade level is this for?
It fits Algebra 1 units on quadratic graphs, Integrated Math 2, and Algebra 2 review. Level 1 works well as an introduction to vertex form and basic shifts.
Still working through transformations?
If a student is doing the shifts correctly but keeps flipping the sign of h, or the graphing is where it falls apart, a few sessions with a tutor usually clears it up faster than another worksheet. We tutor math in person and online across Fremont, Newark and Union City.
