Free Printable WorksheetMathAlgebra IIMath CurriculumA-REI.11

ALG2.105 Linking Solutions to 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 ALG2.105 Linking Solutions to Intersections. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

ALG2.105 Linking Solutions to Intersections - Select the statement that correctly relates solutions of quadratic equations to x-intercepts and to intersections in systems of equations. Associated source-listed standards: CCSS A-REI.11; CA CCSSM A-REI.11; MA 2017 A-REI.11; NY NGLS A-REI.11; 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 ALG2.105 Linking Solutions to Intersections skill assessments:

Problem 1Difficulty: Mastery

Three cases are listed for a quadratic q(x): Case 1 has no real solutions to q(x) = 0. Case 2 has one repeated real solution. Case 3 has two distinct real solutions. Which statement matches the graph of y = q(x) to these cases?

ACase 1: one x-intercept; Case 2: no x-intercepts; Case 3: one touch point.

BCase 1: two x-intercepts; Case 2: one y-intercept; Case 3: no x-intercepts.

CAll three cases have the same graph behavior because they are all quadratics.

DCase 1: no x-intercepts; Case 2: one touch point on the x-axis; Case 3: two x-intercepts.

Solution & Explanation:Real solutions to q(x) = 0 are exactly the x-values where the graph meets the x-axis. So 0, 1 repeated, and 2 distinct real solutions correspond to 0, 1, and 2 x-axis contact points respectively.

Problem 2Difficulty: Mastery

If the x-values solving f(x) = g(x) are 2 - sqrt(3) and 2 + sqrt(3), what must be true?

AThe graphs have y-intercepts 2 - sqrt(3) and 2 + sqrt(3).

BThe graphs intersect only once because radicals are not real numbers.

CThe graphs intersect at two real points whose x-coordinates are 2 - sqrt(3) and 2 + sqrt(3).

DThe common y-value must also be 2 - sqrt(3) and 2 + sqrt(3).

Solution & Explanation:The solutions to f(x) = g(x) are x-values, even when they are irrational. Those x-values identify the vertical locations where the graphs share a point.

Problem 3Difficulty: Mastery

For the system y = x² - 6x + 9 and y = k, when does the system have two real solutions?

AWhen k = 0

BWhen k > 0

CWhen k < 0

DFor every real value of k

Solution & Explanation:The parabola is y = (x - 3)², whose minimum value is 0. A horizontal line y = k intersects it twice only when k is above the minimum, so k > 0.

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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 (Select the statement that correctly relates solutions of quadratic equations to x-intercepts and to intersections in systems of equations. Associated source-listed standards: CCSS A-REI.11; CA CCSSM A-REI.11; MA 2017 A-REI.11; NY NGLS A-REI.11; TX TEKS Algebra II: §111.40.).