Free Printable WorksheetMathAlgebra IIMath CurriculumF-IF.4–5

ALG2.65 Graph Features and Key Characteristics Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.65 Graph Features and Key Characteristics. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.65 Graph Features and Key Characteristics - Identify intercepts, maxima and minima, intervals of increase and decrease, and end behavior from a graph or function description. Associated source-listed standards: CCSS F-IF.4–5; F-IF.7; CA CCSSM F-IF.4–5; F-IF.7; MA 2017 F-IF.4–5; F-IF.7; NY NGLS F-IF.4–5; F-IF.7; TX TEKS Algebra II: §111.40.

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

Algebra II

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 ALG2.65 Graph Features and Key Characteristics skill assessments:

Problem 1Difficulty: Mastery
A polynomial graph rises on the far left, falls after x = -3, rises after x = 1, and falls again after x = 5. Which answer correctly identifies the relative extrema?
AMaximum at x = -3, minimum at x = 1, maximum at x = 5
BMinimum at x = -3, maximum at x = 1, minimum at x = 5
CMaximum at x = -3 and minimum at x = 5 only
DMinimum at x = -3 and maximum at x = 5 only
Solution & Explanation:The graph changes from increasing to decreasing at x = -3, so that is a maximum. It changes from decreasing to increasing at x = 1, so that is a minimum. It changes from increasing to decreasing at x = 5, so that is another maximum.
Problem 2Difficulty: Mastery
A classmate says that the y-intercept of y = (x - 4)2 - 7 is 4 because the graph is shifted right 4 units. Is the classmate correct?
ATrue
BFalse
Solution & Explanation:The y-intercept is found by substituting x = 0. That gives y = (0 - 4)2 - 7 = 16 - 7 = 9, so the claim is false.
Problem 3Difficulty: Mastery
A graph has x-intercepts at -2 and 6 and a maximum at x = 2. If the graph passes through (0, 12), what is the maximum value?
Solution & Explanation:Use y = a(x + 2)(x - 6). Since (0, 12) is on the graph, 12 = a(2)(-6), so a = -1. At x = 2, y = -(4)(-4) = 16, which is the maximum value.

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Frequently Asked Questions

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QHow do I download and print this ALG2.65 Graph Features and Key Characteristics worksheet?

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QIs this ALG2.65 Graph Features and Key Characteristics worksheet free for teachers and homeschoolers?

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra II Math students. It aligns with educational standard F-IF.4–5 (Identify intercepts, maxima and minima, intervals of increase and decrease, and end behavior from a graph or function description. Associated source-listed standards: CCSS F-IF.4–5; F-IF.7; CA CCSSM F-IF.4–5; F-IF.7; MA 2017 F-IF.4–5; F-IF.7; NY NGLS F-IF.4–5; F-IF.7; TX TEKS Algebra II: §111.40.).

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