Free Printable WorksheetMathAlgebra IIMath CurriculumA-REI.4b

ALG2.106 Using the Discriminant to Predict Graph Intersections Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Algebra II Math worksheet provides structured practice on ALG2.106 Using the Discriminant to Predict Graph Intersections. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.106 Using the Discriminant to Predict Graph Intersections - Select the correct use of the discriminant to predict whether a parabola will intersect the x-axis (two, one, or zero real intersections). Associated source-listed standards: CCSS A-REI.4b; F-IF.7a; CA CCSSM A-REI.4b; F-IF.7a; MA 2017 A-REI.4b; F-IF.7a; NY NGLS A-REI.4b; F-IF.7a; 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

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Below are sample questions representative of the exercises included on this worksheet and related ALG2.106 Using the Discriminant to Predict Graph Intersections skill assessments:

Problem 1Difficulty: Mastery
What does the discriminant predict for every real n in y = x2 + 2nx + n2 + 3?
AThe graph has no real x-axis intersections for every real n.
BThe graph touches the x-axis once for every real n.
CThe graph crosses the x-axis twice for every real n.
DThe graph's x-axis behavior depends on n.
Solution & Explanation:The discriminant is (2n)2 - 4(1)(n2 + 3) = 4n2 - 4n2 - 12 = -12. Since it is always negative, every graph in the family has no real x-axis intersections.
Problem 2Difficulty: Mastery
Consider y = (x - r)2 + 7. Which statement is true about its graph for all real r?
AIt can never be tangent to the x-axis for any real r.
BIt is tangent to the x-axis for every real r.
CIt crosses the x-axis twice for every real r.
DIts x-axis behavior depends on whether r is positive.
Solution & Explanation:Expanding gives y = x2 - 2rx + (r2 + 7). The discriminant is (-2r)2 - 4(1)(r2 + 7) = -28, which is always negative. So the graph can never be tangent to or cross the x-axis.
Problem 3Difficulty: Mastery
Which equation is guaranteed to have the same number of x-axis intersections as y = x2 - 8x + 12?
Ay = x2 + 8x + 12
By = x2 - 8x + 16
Cy = x2 - 8x + 20
Dy = 2x2 - 8x + 12
Solution & Explanation:The original equation has discriminant 64 - 48 = 16, so it has two x-axis intersections. y = x2 + 8x + 12 also has discriminant 64 - 48 = 16, so it has the same number of x-axis intersections.

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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.4b (Select the correct use of the discriminant to predict whether a parabola will intersect the x-axis (two, one, or zero real intersections). Associated source-listed standards: CCSS A-REI.4b; F-IF.7a; CA CCSSM A-REI.4b; F-IF.7a; MA 2017 A-REI.4b; F-IF.7a; NY NGLS A-REI.4b; F-IF.7a; TX TEKS Algebra II: §111.40.).

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