What is the connection between the quadratic formula and the types of solutions of a quadratic equation? Guide young mathematicians through this discovery as they use the discriminant to determine the number and types of solutions, and to determine if they are rational or irrational. Learners also make a connection to the graph of the equation. 

Concepts

quadratic formula, solving quadratics, discriminant, x-intercepts

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Additional Tags

math

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Instructional Ideas

• Give examples of discriminants and graphs for repetitive practice until students are proficient with identifying the number and types of solutions
• After finding solutions, ask learners to provide a rough sketch of the graph of the equation

Classroom Considerations

• Requires prior knowledge of the quadratic formula prior
• The sixteenth installment in a 26-part series

Pros

• Care is taken to make connections between the equation, formula, and graph
• Handouts, keys, and thorough teacher guide are provided

Cons

• None

Common Core

HSN-RN.B.3 HSA-SSE.A.1.a HSA-SSE.A.2 HSA-SSE.B.3.a HSA-SSE.B.3.b HSA-APR.B.3 HSA-CED.A.1 HSA-CED.A.2 HSA-REI.B.4.a HSF-IF.B.4 HSF-IF.B.6 HSF-IF.C.7.a HSF-IF.C.8.a