Worksheets · Algebra 2

Graphing polynomial functions worksheet for Algebra 2

Factored form hands you the zeros, so factor a standard-form polynomial first, and the degree and the leading sign tell you what the two ends do. Mark the zeros, decide the ends, and the curve has to weave between them.

Also taught in Precalculus, at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Polynomial Functions

Date Period

Graph each function.

  1. Graph a polynomial in factored form

    Graph y=−(x+2)(x−1)(x−2)−10−10−5−5551010
  2. Graph y=−(x+3)(x+2)(x−1)−10−10−5−5551010
  3. Graph y=(x+1)x(x−1)−10−10−5−5551010
  4. Graph y=(x+3)(x+1)(x−1)−10−10−5−5551010
  5. Graph y=−(x+3)(x+1)x−10−10−5−5551010
  6. Graph y=−x(x−1)(x−3)−10−10−5−5551010
  7. Graph y=−(x+1)x(x−1)−10−10−5−5551010
  8. Graph y=(x+1)(x−2)(x−3)−10−10−5−5551010
  9. Graph y=(x+2)(x+1)x−10−10−5−5551010
  10. Graph y=x(x−2)(x−3)−10−10−5−5551010

  1. Graph a polynomial in standard form

    Graph y=−x3−x2+4x+4−10−10−5−5551010
  2. Graph y=−x3+2x2+3x−10−10−5−5551010
  3. Graph y=x3−x−10−10−5−5551010
  4. Graph y=−x3+x−10−10−5−5551010
  5. Graph y=x3−x2−4x+4−10−10−5−5551010
  6. Graph y=x3+2x2−x−2−10−10−5−5551010
  7. Graph y=x3+2x2−3x−10−10−5−5551010
  8. Graph y=−x3+x2+2x−10−10−5−5551010
  9. Graph y=−x3+2x2+5x−6−10−10−5−5551010
  10. Graph y=x3−x2−6x−10−10−5−5551010

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

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Polynomial FunctionsAnswer keyVersion 1

Date Period

Graph each function.

  1. Graph a polynomial in factored form

    Graph y=−(x+2)(x−1)(x−2)−10−10−5551010−5Zeros −2,1,2; rises to the left, falls to the right
  2. Graph y=−(x+3)(x+2)(x−1)−10−10−5−5510105Zeros −3,−2,1; rises to the left, falls to the right
  3. Graph y=(x+1)x(x−1)−10−10−5−5551010Zeros −1,0,1; falls to the left, rises to the right
  4. Graph y=(x+3)(x+1)(x−1)−10−10−5−5551010Zeros −3,−1,1; falls to the left, rises to the right
  5. Graph y=−(x+3)(x+1)x−10−10−5−5551010Zeros −3,−1,0; rises to the left, falls to the right
  6. Graph y=−x(x−1)(x−3)−10−10−5−5510510Zeros 0,1,3; rises to the left, falls to the right
  7. Graph y=−(x+1)x(x−1)−10−10−5−5551010Zeros −1,0,1; rises to the left, falls to the right
  8. Graph y=(x+1)(x−2)(x−3)−10−551010−10−55Zeros −1,2,3; falls to the left, rises to the right
  9. Graph y=(x+2)(x+1)x−10−10−5−5551010Zeros −2,−1,0; falls to the left, rises to the right
  10. Graph y=x(x−2)(x−3)−10−5551010−10−5Zeros 0,2,3; falls to the left, rises to the right

  1. Graph a polynomial in standard form

    Graph y=−x3−x2+4x+4−10−10−5−5551010zeros −2,−1,2; rises to the left, falls to the right
  2. Graph y=−x3+2x2+3x−10−10−5−5551010zeros −1,0,3; rises to the left, falls to the right
  3. Graph y=x3−x−10−10−5−5551010zeros −1,0,1; falls to the left, rises to the right
  4. Graph y=−x3+x−10−10−5−5551010zeros −1,0,1; rises to the left, falls to the right
  5. Graph y=x3−x2−4x+4−10−10−5−5551010zeros −2,1,2; falls to the left, rises to the right
  6. Graph y=x3+2x2−x−2−10−10−5−5551010zeros −2,−1,1; falls to the left, rises to the right
  7. Graph y=x3+2x2−3x−10−10−5−5551010zeros −3,0,1; falls to the left, rises to the right
  8. Graph y=−x3+x2+2x−10−10−5−5551010zeros −1,0,2; rises to the left, falls to the right
  9. Graph y=−x3+2x2+5x−6−10−10−5551010−5zeros −2,1,3; rises to the left, falls to the right
  10. Graph y=x3−x2−6x−10−10−5−5551010zeros −2,0,3; falls to the left, rises to the right

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

How to do these

Graph y=(x+2)(x−1)(x−3)

  1. The zeros are -2, 1 and 3.
  2. Three factors and a positive lead, so it comes up from the bottom left and leaves top right.
  3. It crosses at each zero, so it turns twice between them.

The answer is Zeros −2,1,3; falls to the left, rises to the right.

Where students go wrong

Getting the ends the wrong way round. An odd number of factors sends the two ends opposite ways and an even number sends them the same way, with the leading sign deciding which. The other slip is forgetting the curve has to turn between consecutive zeros.

Also called polynomial graphs, end behavior graphs or plotting polynomials from factors.

What you can put on this worksheet

A polynomial from its factors
Graph y=−x(x−2) → Zeros 0,2; falls at both ends
From standard form, factored first
Graph y=−x3−x2+6x → zeros −3,0,2; rises to the left, falls to the right
Calculator zeros and extrema to the nearest tenth
Use a graphing calculator to find the relative maxima and minima to the nearest tenth: f(x)=x4+x3−5x+3 → Maximum: noneMinimum: (0.9,−0.1)

Questions about these worksheets

Yes. Every graphing polynomial functions 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 2 is usually taken around 10th or 11th 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 polynomial functions 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.

You pick from 3: a polynomial from its factors, from standard form, factored first and calculator zeros and extrema to the nearest tenth. Tick as many as you want and set how many of each, or let it spread them evenly.

Getting the ends the wrong way round. An odd number of factors sends the two ends opposite ways and an even number sends them the same way, with the leading sign deciding which. The other slip is forgetting the curve has to turn between consecutive zeros.