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ALG1.93 Quadratic Word Problems and Reasonableness Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.93 Quadratic Word Problems and Reasonableness. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.93 Quadratic Word Problems and Reasonableness - Select the option that shows how to model a situation with a quadratic equation or function; Select the statement that correctly interprets which solutions make sense and explain why others are extraneous. (CCSS: A-APR.3; F-BF.1a; TEKS: §111.39(c)(6)(B–C), (7)(A); VA SOL: A.F.2 d; FL B.E.S.T.: MA.912.AR.3.5; NY-NGLS: AI-A.APR.3, AI-F.BF.1a; CA CCSSM: A-APR.3; MA 2017: HS.A-APR.3; DoDEA CCRSM; NAEP: Algebra—modeling; NCTM P2A: Practices 4, 6.)

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 I

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

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Below are sample questions representative of the exercises included on this worksheet and related ALG1.93 Quadratic Word Problems and Reasonableness skill assessments:

Problem 1Difficulty: Mastery
A ball is dropped from 144 feet, so its height can be modeled by h(t) = 144 - 16t2. Solving h(t) = 0 gives t = -3 and t = 3. Which option gives the correct model interpretation?
Ah(t) = 144 + 16t2, and both times are reasonable
Bh(t) = -144 + 16t2, and t = -3 seconds is the landing time
Ch(t) = 16t2 - 144t, and neither time is reasonable
Dh(t) = 144 - 16t2, and t = 3 seconds is reasonable while t = -3 seconds is extraneous
Solution & Explanation:A dropped object starts at 144 feet and accelerates downward, so h(t) = 144 - 16t2. The positive root t = 3 seconds is the landing time; negative time is extraneous.
Problem 2Difficulty: Mastery
A revenue function is R(p) = -2(p - 18)2 + 648, where p is the price in dollars. Solving R(p) = 486 gives p = 9 and p = 27. Which statement is correct?
AOnly p = 9 is reasonable because it is less than the maximizing price.
BOnly p = 27 is reasonable because it is greater than the maximizing price.
CBoth prices are extraneous because revenue cannot be modeled in vertex form.
DBoth prices are reasonable because they are positive and produce the same revenue on opposite sides of the maximum.
Solution & Explanation:The vertex is at p = 18, and equal revenues can occur at prices equally far from the vertex. Both $9 and $27 are positive prices, so both are reasonable.
Problem 3Difficulty: Mastery
A path is built inside a 30-foot by 20-foot rectangular park, leaving a central grassy area of 416 square feet. If x is the uniform path width, solving (30 - 2x)(20 - 2x) = 416 gives x = 2 and x = 23. Which interpretation is correct?
Ax = 2 feet is reasonable, and x = 23 feet is extraneous because it would make a negative dimension.
Bx = 23 feet is reasonable because it is a root.
CBoth roots are possible path widths.
DNeither root works because the path is inside the park.
Solution & Explanation:An inside path reduces each dimension by 2x, so x must be less than 10 feet. The width x = 2 works; x = 23 would make the central dimensions negative.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Algebra I Math students. It aligns with educational standard A-APR.3 (Primary standard selected for prompt fields in this prompt cell: CCSS A-APR.3. Skill statement in this prompt cell: Select the option that shows how to model a situation with a quadratic equation or function; Select the statement that correctly interprets which solutions make sense and explain why others are extraneous. Associated standards listed with this skill in the curriculum source: CCSS: A-APR.3; F-BF.1a; TEKS: §111.39(c)(6)(B–C), (7)(A); VA SOL: A.F.2 d; FL B.E.S.T.: MA.912.AR.3.5; NY-NGLS: AI-A.APR.3, AI-F.BF.1a; CA CCSSM: A-APR.3; MA 2017: HS.A-APR.3; DoDEA CCRSM; NAEP: Algebra—modeling; NCTM P2A: Practices 4, 6. Use this prompt-provided wording as the supporting standard description for this workflow.).

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