Matching worksheet
7 pages. Three levels with lettered graphs, scrambled equations and properties, and space to explain two matches. No cutting needed.
Algebra 2 · Free printable
Polynomial Graph Matching Worksheet and Card Sort
Match polynomial graphs to equations using zeros, multiplicity, and end behavior. Use the worksheet for independent practice or the card sort for partner work. Both formats include three levels, with answers in the teacher guide.
14 functions · Three levels · About 20–50 minutes
Free classroom use. No signup or email address required.
Download the PDFs
Choose the worksheet if you want students to write their answers on the page. Choose the cards if you want them to sort and discuss their matches. Both use the same functions.
Get the worksheet PDF →
Printable card sort
18 pages. 112 cards across three levels, plus recording sheets. Print single-sided at 100%, then cut along the dashed lines.
Teacher guide and answer key
6 pages. Instructions, pacing suggestions, and answers for both formats, including the card codes and worksheet option numbers.
Complete bundle
31 pages. The three separate PDFs combined into one file: student cards, worksheets, teacher instructions, and answers.
The cards are labeled by category, so color printing is optional. If you only need one worksheet level, print pages 2–3 for the introductory set, 4–5 for standard Algebra 2, or 6–7 for the challenge set.
Choose a level
The activity is intended for Algebra 2. The introductory set offers a shorter starting point; the challenge set also works for precalculus review.
| Level | Functions | What changes |
|---|---|---|
| Introductory | 4 quadratics and cubics | Degrees 2–3, integer zeros, leading coefficients ±1, and two examples with double roots. |
| Standard Algebra 2 | 5 cubics and quartics | Degrees 3–4, double and triple roots, and leading coefficients ±1 and ±2. |
| Challenge | 5 quartics and quintics | Degrees 4–5, multiplicities up to 4, and one fractional leading coefficient. |
Allow about 20–30 minutes for the introductory set and 30–50 minutes for the other levels, including discussion. If you are unsure where to start, use the polynomial skills diagnostic first.
How to match a polynomial to its graph
- Check the zeros. Read the x-intercepts from the graph and compare them with the factors. A factor of (x − r) gives a zero at x = r.
- Look at each intercept. A crossing means odd multiplicity. A touch and turn means even multiplicity. This tells you whether the multiplicity is odd or even; it does not give the exact number by itself.
- Check both tails. Use the degree and the sign of the leading coefficient to predict the end behavior. The tails can confirm degree parity and leading sign, but cannot tell you the exact degree.
- Test a point. Substitute an easy x-value whose point is visible on the graph. The y-intercept is often a good choice. If the equation and graph disagree there, reconsider the match.
For a shorter first round, use just the graph and factored-form cards. Add the other categories once those matches are secure. The full sort includes expanded equation, factored form, graph, zeros, multiplicity, end behavior, degree, and leading coefficient.
A worked match
This example is separate from the printable sets.
y = (x + 1)(x − 3)2
The graph must cross the x-axis at −1 and touch it at 3. The degree is 3 and the leading coefficient is +1, so the left tail points down and the right tail points up.
Check x = 0: the equation gives y = 9. A graph with the right zeros but a different y-intercept would not be a match.
Using the activity in class
Students should be comfortable reading intercepts and connecting factors with zeros. It helps to introduce repeated roots before using the full set. If factoring is still the sticking point, start with the factoring guide and practice worksheets.
Partner work
Give each pair one level and sort the cards into category stacks. Have students take turns proposing a match and explaining the evidence. Before they record it, both partners should be able to explain why it works.
Independent practice
Use the no-cut worksheet for classwork, review, or a substitute lesson. Students write the graph letters beside the matching representations and finish with two written explanations.
Watch the reasoning, not just the answers. Ask a student to explain a flattened crossing, or to predict the tails before checking the graph. Counting intercepts is not enough to determine degree, and knowing the degree alone is not enough to determine both tail directions.
Some degree, leading-coefficient, and end-behavior cards are identical. Those copies are interchangeable. Accept another valid arrangement when the properties agree and each copy is used once.
Skills covered: zeros and factors, multiplicity, end behavior, and connections between equations and graphs. These support CCSS HSA.APR.B.3 and HSF.IF.C.7c.
Answer-key preview
These are the four functions on the introductory student page shown above. The teacher PDF includes the complete matches, card codes, and worksheet option numbers for all three levels.
| Graph | Factored equation | Zeros | End behavior |
|---|---|---|---|
| A | y = (x + 2)(x − 1) | −2, 1; both simple | Left up; right up |
| B | y = −(x − 1)2 | 1; double | Left down; right down |
| C | y = (x + 1)2(x − 2) | −1 double; 2 simple | Left down; right up |
| D | y = −(x + 2)(x − 1)(x − 3) | −2, 1, 3; all simple | Left up; right down |