Polynomials
Identifying polynomial degree worksheets
Find the degree of ten monomials and polynomials. Select one through six terms, compare term degrees and check a separate key with the exponent calculations.
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Polynomial graph identification worksheets
Match expanded linear, quadratic, cubic and quartic equations to one of four coordinate graphs drawn on the same −5 to 5 scale, with balanced answer positions and deliberately useful distractors.
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Choose the graph A-D that represents each expanded polynomial function y = p(x). All plots use the same -5 to 5 scale.
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Customize this worksheetMatch coefficients to the whole curve
Every question prints an expanded equation and four graphs on the same square scale. Use the constant term for the y-intercept, the degree and leading sign for end behavior, and exact values such as p(1) or p(−1) to distinguish similar choices.
At least one distractor shares the y-intercept and another shares the target degree, so neither shortcut is enough by itself. Cubic and quartic sets include both simpler and multi-turn shapes.
Learning objective
What this activity builds
Connect coefficients, intercepts, leading behavior and turning structure to the complete graph of an expanded polynomial function.
Worked example
Which graph represents y = x² − 2x?
Choose the upward-opening graph through (0,0) with vertex (1,−1).
The positive leading coefficient opens upward. Factoring x(x − 2) gives x-intercepts 0 and 2, and the axis halfway between them is x = 1.
Teaching notes
Make the practice count
- Start with the y-intercept p(0), but keep checking because at least one choice shares it.
- Use the degree and leading sign to predict end behavior.
- Evaluate one or two visible x-values to separate graphs with similar shapes.
- A cubic can be monotone or have two turning points; a quartic can have one or several turns.
- Every option uses the same square scale, so steepness and crossing locations are comparable.
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Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose 2, 4, 6, 8 or 10 questions and any nonempty set of target degrees. Every question shows one expanded polynomial and four graphs on the same −5 to 5 scale.
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Polynomials
Descartes Rule of Signs worksheets
Use sign changes in P(x) and P(−x) to list every possible number of positive and negative real zeros for twelve degree-two through degree-six polynomials.
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