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

Pre CAL.53 Analyze Local Extrema and Shape from Polynomial Graphs 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.53 Analyze Local Extrema and Shape from Polynomial Graphs. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Pre-CAL.53 Analyze Local Extrema and Shape from Polynomial Graphs - Primary standard selected for prompt fields in this prompt cell: CCSS HSA-SSE.1-3. Skill statement in this prompt cell: Given a polynomial graph or table, identify intervals of increase and decrease and select the correct location and interpretation of local extrema. 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.53 Analyze Local Extrema and Shape from Polynomial Graphs skill assessments:

Problem 1Difficulty: Mastery
A table of values for a polynomial function is x: -5, -4, -3, -2, -1, 0, 1, 2, 3 and f(x): -8, -2, 4, 9, 5, -1, -4, 0, 7. Which complete summary is correct?
AIncreasing from x = -5 to x = -2, decreasing from x = -2 to x = 1, increasing from x = 1 to x = 3; local maximum at (-2, 9) and local minimum at (1, -4).
BDecreasing from x = -5 to x = -2, increasing from x = -2 to x = 1, decreasing from x = 1 to x = 3; local minimum at (-2, 9) and local maximum at (1, -4).
CIncreasing over the entire listed interval; no local extrema are shown.
DThe only local extremum is at x = 0 because f(0) is negative.
Solution & Explanation:The values rise to 9 at x = -2, fall to -4 at x = 1, and then rise again. That gives a local maximum at (-2, 9) and a local minimum at (1, -4).
Problem 2Difficulty: Mastery
Use the planned graph of y = f(x), which has local maximum (-2, 5), local minimum (1, -4), and then rises without turning through x = 6. Which statement is best?
AThere is a local maximum at x = 6 because the graph is far to the right.
BThere is no local extremum at x = 6 unless the graph changes direction there.
CEvery increasing point after x = 1 is a local minimum.
DThe local minimum value is 1 because the point occurs at x = 1.
Solution & Explanation:A local extremum requires a nearby change in direction. Simply being far to the right or on an increasing part of the graph is not enough.
Problem 3Difficulty: Mastery
A table of values for a polynomial function is x: -4, -3, -2, -1, 0, 1, 2, 3 and f(x): 10, 4, 0, 1, 5, 2, -3, -1. Which option correctly identifies the turns shown?
Alocal minimum at (-2, 0), local maximum at (0, 5), and local minimum at (2, -3)
Blocal maximum at (-2, 0), local minimum at (0, 5), and local maximum at (2, -3)
Clocal maximum at (-3, 4) and local minimum at (1, 2)
Dno turns are shown
Solution & Explanation:The values fall to 0 then rise, rise to 5 then fall, and fall to -3 then rise, giving the three stated turns.

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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 a polynomial graph or table, identify intervals of increase and decrease and select the correct location and interpretation of local extrema. 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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