Free Printable WorksheetMathAlgebra IMath CurriculumF-IF.7a, F-BF.3

ALG1.85 Key Features of Quadratic 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 ALG1.85 Key Features of Quadratic Functions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG1.85 Key Features of Quadratic Functions - Identify the vertex, axis of symmetry, intercepts, and opening direction of a parabola; Select the statement that correctly interprets how these features relate to maximum or minimum values in context. (CCSS: F-IF.7a, F-BF.3; TEKS: §111.39(c)(7)(A–C); VA SOL: A.F.2 b–d; FL B.E.S.T.: MA.912.AR.3.6–3.7; NY-NGLS: AI-F.IF.7a; CA CCSSM: F-IF.7a; MA 2017: HS.F-IF.7a; DoDEA CCRSM; NAEP: Algebra—graphs; NCTM P2A: Practices 2, 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

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Below are sample questions representative of the exercises included on this worksheet and related ALG1.85 Key Features of Quadratic Functions skill assessments:

Problem 1Difficulty: Mastery
A business model uses q(x) = -(x + 2)(x - 8), where q(x) is profit in hundreds of dollars. Which statement correctly summarizes the key features?
AZeros at x = 2 and x = -8, axis x = -3, minimum value 25, and y-intercept (0, -16)
BZeros at x = -2 and x = 8, axis x = 3, minimum value -25, and y-intercept (0, 16)
CZeros at x = -2 and x = 8, axis x = 5, maximum value 16, and y-intercept (0, 25)
DZeros at x = -2 and x = 8, axis x = 3, maximum value 25, and y-intercept (0, 16)
Solution & Explanation:The zeros come from the factors: x = -2 and x = 8. The axis is their average, x = 3. Then q(3) = -(5)(-5) = 25, a maximum because the graph opens downward. The y-intercept is q(0) = -(2)(-8) = 16.
Problem 2Difficulty: Mastery
Use the two graphs shown. Graph B is a vertical shift of Graph A. Which statement correctly describes the shift?
AGraph B is Graph A shifted right 3 units, so its axis changes from x = 1 to x = 4.
BGraph B is Graph A reflected downward, so its maximum value is 1.
CGraph B is Graph A shifted up 3 units, so its minimum value is 1 instead of -2.
DGraph B is Graph A shifted down 3 units, so its minimum value is -5.
Solution & Explanation:Both graphs open upward and have the same axis x = 1. Graph A has vertex (1, -2), and Graph B has vertex (1, 1), so B is A shifted up 3 units and its minimum value increases to 1.
Problem 3Difficulty: Mastery
A student says the vertex y-value of y = -3(x - 1)2 + 12 is the y-intercept. Which complete correction is correct?
AThe vertex is (0, 12), the y-intercept is (1, 12), and the x-intercepts are (-1, 0) and (3, 0).
BThe vertex is (1, 12), the y-intercept is (0, 9), and the x-intercepts are (-1, 0) and (3, 0).
CThe vertex is (1, 12), the y-intercept is (0, 12), and there are no x-intercepts.
DThe vertex is (-1, 12), the y-intercept is (0, 9), and the x-intercepts are (1, 0) and (3, 0).
Solution & Explanation:The vertex form gives vertex (1, 12). The y-intercept is found by setting x = 0: y = -3(1) + 12 = 9. For x-intercepts, set 0 = -3(x - 1)2 + 12, so (x - 1)2 = 4 and x = -1 or 3.

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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 F-IF.7a, F-BF.3 (Primary standard selected for prompt fields in this prompt cell: CCSS F-IF.7a, F-BF.3. Skill statement in this prompt cell: Identify the vertex, axis of symmetry, intercepts, and opening direction of a parabola; Select the statement that correctly interprets how these features relate to maximum or minimum values in context. Associated standards listed with this skill in the curriculum source: CCSS: F-IF.7a, F-BF.3; TEKS: §111.39(c)(7)(A–C); VA SOL: A.F.2 b–d; FL B.E.S.T.: MA.912.AR.3.6–3.7; NY-NGLS: AI-F.IF.7a; CA CCSSM: F-IF.7a; MA 2017: HS.F-IF.7a; DoDEA CCRSM; NAEP: Algebra—graphs; NCTM P2A: Practices 2, 7. Use this prompt-provided wording as the supporting standard description for this workflow.).

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