Challenge the class to utilize their knowledge of linear and quadratic functions to determine the intersection of the parent quadratic graph and linear proportional graphs. Using the pattern for the solutions, individuals develop a general formula for them. Then, using algebraic methods, young mathematicians show their formulas hold true.

Concepts

linear functions, quadratic functions, intersection, graphing systems of equations, systems of equations, linear equations, quadratic equations

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Additional Tags

math

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Instructional Ideas

• Lead a discussion after the task about whether the general solution works if the slope of the linear function is negative
• Use the assessment as a spring board into the discussion of HSA-REI.D.11, finding the solutions for f(x) = g(x)

Classroom Considerations

• Learners should be familiar with working with quadratic equations

Pros

• Contains sample work for various point values
• Provides descriptions of misunderstandings based upon the tasks performance on a national math assessment

Cons

• The mathematical symbols do not display correctly in the rubric

Common Core

HSF-IF.B.4 HSF-IF.B.5 HSF-IF.C.7.a HSF-IF.C.9 MP5 MP7