Free Printable WorksheetMathAlgebra IMath CurriculumA-APR.1, A-SSE.3a, A-APR.3

ALG1.78 Factoring and Zeros of Functions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra I Math worksheet provides structured practice on ALG1.78 Factoring and Zeros of Functions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.78 Factoring and Zeros of Functions - Select the option that shows how to use factoring to identify zeros and x-intercepts of a quadratic function; Select the statement that correctly interprets factors and zeros as solutions in context. (CCSS: A-APR.1, A-SSE.3a, A-APR.3; TEKS: §111.39(c)(10)(A–C); VA SOL: A.EO.2a–e; FL B.E.S.T.: MA.912.AR.1.3–1.4, 1.7; NY-NGLS: AI-A.APR.1, AI-A.APR.3; CA CCSSM: A-APR.1,3; MA 2017: HS.A-APR.1,3; DoDEA CCRSM; NAEP: Algebra—polynomial operations; NCTM P2A: Practices 6, 7.)

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

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 ALG1.78 Factoring and Zeros of Functions skill assessments:

Problem 1Difficulty: Mastery
A graph shows a projectile model with x-intercepts at (0, 0) and (12, 0), opening downward. Which contextual statement is best supported?
AThe projectile reaches maximum height at t=0 seconds and t=12 seconds.
BThe projectile is at ground level at t=-12 seconds and t=12 seconds.
CThe x-intercepts mean the projectile's height is 0 and 12 feet.
DThe projectile is at ground level at t=0 seconds and t=12 seconds.
Solution & Explanation:The x-intercepts are time values where height equals 0. A downward projectile graph crossing at t=0 and t=12 means it starts at ground level and returns to ground level at 12 seconds.
Problem 2Difficulty: Mastery
Determine whether this statement is true or false: The zeros of f(x)=2x(x - 7) are the solutions of 2x(x - 7)=0, not the y-intercepts of the graph.
AFalse; this statement treats the constants in the factors as the zeros without solving: The zeros of f(x)=2x(x - 7) are the solutions of 2x(x - 7)=0, not the y-intercepts of the graph.
BFalse; this statement confuses zeros with y-intercepts: The zeros of f(x)=2x(x - 7) are the solutions of 2x(x - 7)=0, not the y-intercepts of the graph.
CTrue; this statement is supported by setting the relevant factor or factors equal to 0: The zeros of f(x)=2x(x - 7) are the solutions of 2x(x - 7)=0, not the y-intercepts of the graph.
DFalse; this statement cannot apply to a quadratic function: The zeros of f(x)=2x(x - 7) are the solutions of 2x(x - 7)=0, not the y-intercepts of the graph.
Solution & Explanation:Zeros are x-values that make the output 0. The y-intercept is where x=0, while zeros correspond to x-intercepts.
Problem 3Difficulty: Mastery
Which pair of functions has exactly the same x-intercepts?
Af(x)=(x + 1)(x - 4) and g(x)=(x - 1)(x + 4)
Bf(x)=(x + 1)(x - 4) and g(x)=-3(x + 1)(x - 4)
Cf(x)=(x + 1)(x - 4) and g(x)=3(x + 2)(x - 4)
Df(x)=(x + 1)(x - 4) and g(x)=(x + 1)(x + 4)
Solution & Explanation:Multiplying by -3 changes the graph's stretch and reflection but not the zeros. Both functions in choice B have zeros -1 and 4.

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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.1, A-SSE.3a, A-APR.3 (Primary standard selected for prompt fields in this prompt cell: CCSS A-APR.1, A-SSE.3a, A-APR.3. Skill statement in this prompt cell: Select the option that shows how to use factoring to identify zeros and x-intercepts of a quadratic function; Select the statement that correctly interprets factors and zeros as solutions in context. Associated standards listed with this skill in the curriculum source: CCSS: A-APR.1, A-SSE.3a, A-APR.3; TEKS: §111.39(c)(10)(A–C); VA SOL: A.EO.2a–e; FL B.E.S.T.: MA.912.AR.1.3–1.4, 1.7; NY-NGLS: AI-A.APR.1, AI-A.APR.3; CA CCSSM: A-APR.1,3; MA 2017: HS.A-APR.1,3; DoDEA CCRSM; NAEP: Algebra—polynomial operations; NCTM P2A: Practices 6, 7. Use this prompt-provided wording as the supporting standard description for this workflow.).

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