Free Printable WorksheetMathAlgebra IIMath CurriculumA-REI.11

ALG2.101 Estimating Solutions Graphically Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.101 Estimating Solutions Graphically. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.101 Estimating Solutions Graphically - Approximate roots from graphs or tables and refine or confirm with algebraic methods or technology. Associated source-listed standards: CCSS A-REI.11; MP.5; CA CCSSM A-REI.11; MP.5; MA 2017 A-REI.11; MP.5; NY NGLS A-REI.11; MP.5; 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 ALG2.101 Estimating Solutions Graphically skill assessments:

Problem 1Difficulty: Mastery

To solve q(x) = l(x), a graph first shows a larger intersection between x = 6.4 and x = 6.5. A zoom table then gives q(6.43) = 9.18 and l(6.43) = 9.27; q(6.44) = 9.25 and l(6.44) = 9.24; and q(6.45) = 9.32 and l(6.45) = 9.21. Estimate the larger solution to the nearest hundredth.

Solution & Explanation:The solution occurs where q(x) and l(x) are equal. At x = 6.44 the values are closest and switch order across the interval, so 6.44 is the best estimate.

Problem 2Difficulty: Mastery

A company's profit graph is quadratic. The graph shows P(x) = 0 once between x = 12 and x = 13 and again between x = 27 and x = 28. A zoomed view suggests the crossings are near x = 12.4 and x = 27.6. Which pair best estimates the break-even values?

A13.0 and 27.0

B11.8 and 28.2

C20.0 and 20.0

D12.4 and 27.6

Solution & Explanation:Break-even points are where P(x) = 0. The zoomed values place the intersections near 12.4 and 27.6, so that pair is the best estimate.

Problem 3Difficulty: Mastery

A parabola intersects y = 5 twice and has axis of symmetry x = 4.10. A zoomed table near the left intersection gives q(2.46) = 5.05, q(2.47) = 5.01, and q(2.48) = 4.96. Estimate the right intersection x-value to the nearest hundredth.

Solution & Explanation:The left intersection is best estimated by x = 2.47 because q(2.47) is closest to 5. Points at the same height are symmetric about x = 4.10, so the right intersection is 4.10 + (4.10 - 2.47) = 5.73.

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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 Algebra II Math students. It aligns with educational standard A-REI.11 (Approximate roots from graphs or tables and refine or confirm with algebraic methods or technology. Associated source-listed standards: CCSS A-REI.11; MP.5; CA CCSSM A-REI.11; MP.5; MA 2017 A-REI.11; MP.5; NY NGLS A-REI.11; MP.5; TX TEKS Algebra II: §111.40.).