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1 Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 5. Capstone Problem — Curves Ahead; Task 3.5.2 TASK 3.5.2: DISCUSSION AND DISCOVERY 1. Discuss the use of triangles, circles, parallelograms, trapezoids, etc. to develop real world application problems that depend on a quadratic equation and its zeros. What are the limitations of the geometric shapes and how does the quadratic equation have to be chosen to accommodate them? 2. Task 3.5.1 was developed around the general form of the quadratic equation. Discuss the advantages of examining the vertex form y = a(x ! h)2 + k over the general form y = Ax 2 + Bx + C . Modify task 3.5.1 using the vertex form instead of the general form so that these advantages are discovered. November 24, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at Austin for the Texas Higher Education Coordinating Board. 2 Algebra I: Strand 3. Quadratic and Nonlinear Functions; Topic 5. Capstone Problem — Curves Ahead; Task 3.5.2 3. High school algebra students are introduced to quadratic equations in three different forms: (1) y = ax 2 + bx + c (2) y = a(x ! h)2 + k (3) y = ax 2 + c Discuss the similarities and differences of these representations. Explain why Algebra 1 students are only introduced to form (3) while Algebra 2 students primarily see forms (1) and (2). What information can be gained about the graph of each quadratic from each of these forms? No solutions to these problems are included. They are intended to be ideas for group discussions. November 24, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at Austin for the Texas Higher Education Coordinating Board.