Students apply their experiences from Topic A as they transform quadratic functions from standard form to vertex form in Topic B. The strategy known as completing the square is used to solve quadratic equations when the quadratic expression cannot be factored (A-SSE.B.3b). Students recognize that this form reveals specific features of quadratic functions and their graphs, namely the minimum or maximum of the and the line of symmetry of the graph (A-APR.B.3, F-IF.B.4, F-IF.C.7a).
Students derive the quadratic formula by completing the square for a general quadratic equation in standard form and use it to determine the nature and number of solutions for equations when y equals zero (A-SSE.A.2, A-REI.B.4). For quadratics with irrational roots, students use the quadratic formula and explore the properties of irrational numbers (N-RN.B.3).
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