Free Printable WorksheetMathPre-CalculusMath CurriculumHSA-SSE.1-3

Pre CAL.52 Create Polynomial Functions with Given Zeros and End Behavior Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Pre-Calculus Math worksheet provides structured practice on Pre CAL.52 Create Polynomial Functions with Given Zeros and End Behavior. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.52 Create Polynomial Functions with Given Zeros and End Behavior - Primary standard selected for prompt fields in this prompt cell: CCSS HSA-SSE.1-3. Skill statement in this prompt cell: Given desired zeros, multiplicities, and end behavior, select the polynomial function that satisfies all conditions and matches the corresponding graph. Associated standards listed with this skill in this prompt cell: CCSS HSA-SSE.1-3; CCSS HSA-APR.1-7(+); CCSS HSF-IF.7c-7d,8a; CCSS HSA-REI.11; SMP 1,2,7,8; AP Precalculus CED Unit 1; TX §111.42(c)(5)(B-H); FL MA.912.AR.6.3-6.6, MA.912.AR.8.3; VA MA.CF.1. Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Pre-Calculus

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related Pre CAL.52 Create Polynomial Functions with Given Zeros and End Behavior skill assessments:

Problem 1Difficulty: Mastery
A least-degree polynomial has zeros -3, 0 with multiplicity 2, 1/2, 5 with multiplicity 2, end behavior both ends up, and passes through (1, 32). Which function matches all conditions?
Af(x) = -(1/2)(x + 3)x2(2x - 1)(x - 5)2
Bf(x) = (x + 3)x2(2x - 1)(x - 5)2
Cf(x) = (1/2)(x - 3)x2(2x - 1)(x - 5)2
Df(x) = (1/2)(x + 3)x2(2x - 1)(x - 5)2
Solution & Explanation:Each zero becomes a factor, and the exponent on that factor gives the required multiplicity. The factors for zeros -3, 0 with multiplicity 2, 1/2, 5 with multiplicity 2 give f(x) = (1/2)(x + 3)x2(2x - 1)(x - 5)2. Its degree is 6, so the sign of the leading coefficient gives both ends up. Substituting x = 1 gives f(1) = 32, so the scale factor is correct.
Problem 2Difficulty: Mastery
Which answer choice gives a valid least-degree polynomial with zeros -5 with multiplicity 3, -1 with multiplicity 2, 2 and end behavior both ends down?
Af(x) = (x + 5)3(x + 1)2(x - 2)
Bf(x) = -(x - 5)3(x + 1)2(x - 2)
Cf(x) = -(x + 5)3(x + 1)2(x - 2)
Df(x) = -(x + 5)2(x + 1)2(x - 2)
Solution & Explanation:Each zero becomes a factor, and the exponent on that factor gives the required multiplicity. The factors in f(x) = -(x + 5)3(x + 1)2(x - 2) give zeros -5 with multiplicity 3, -1 with multiplicity 2, 2. The total degree is 6, and the leading coefficient sign gives both ends down.
Problem 3Difficulty: Mastery
Use the graph shown. The graph has both ends up; the curve touches at x = -4 and x = 1 and crosses at x = 0 and x = 6. Which polynomial function matches the graph?
Af(x) = -(x + 4)2x(x - 1)2(x - 6)
Bf(x) = (x + 4)2x(x - 1)2(x - 6)
Cf(x) = (x - 4)2x(x - 1)2(x - 6)
Df(x) = (x + 4)x(x - 1)2(x - 6)
Solution & Explanation:Touching the x-axis means an even multiplicity; crossing means an odd multiplicity, and a flattened crossing is usually multiplicity 3. The factors in f(x) = (x + 4)2x(x - 1)2(x - 6) give zeros -4 with multiplicity 2, 0, 1 with multiplicity 2, 6. The total degree is 6, and the leading coefficient sign gives both ends up.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Pre-Calculus Math students. It aligns with educational standard HSA-SSE.1-3 (Primary standard selected for prompt fields in this prompt cell: CCSS HSA-SSE.1-3. Skill statement in this prompt cell: Given desired zeros, multiplicities, and end behavior, select the polynomial function that satisfies all conditions and matches the corresponding graph. Associated standards listed with this skill in this prompt cell: CCSS HSA-SSE.1-3; CCSS HSA-APR.1-7(+); CCSS HSF-IF.7c-7d,8a; CCSS HSA-REI.11; SMP 1,2,7,8; AP Precalculus CED Unit 1; TX §111.42(c)(5)(B-H); FL MA.912.AR.6.3-6.6, MA.912.AR.8.3; VA MA.CF.1. Use this prompt-provided wording as the supporting standard description for this workflow.).

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