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Students determine a plan to maximize profit on a donut sale using data provided. The parabolic graphs of selling price vs.
Students determine a plan to maximize profit on a donut sale using data provided. The parabolic graphs of selling price vs. income and selling price vs. profit are used to explore intercepts, symmetry, and the vertex. The graphs and table allow for a side-by-side comparison of linear and quadratic functions. The goal is for students to link representations of data through tables and graphs and to see the connection to algebraic solutions. A quadratic rule is generated using the idea that income is selling price multiplied by number sold. This problem is suited to an introduction of quadratic functions after a study of quadratic equations. An activity sheet and solutions are included. This mathematically rich problem was developed for the Ohio Resource Center to accompany the Mathematics Program Models for Ohio High Schools proposed by the Ohio Department of Education. (author/sw)
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| Mathematics Academic Content Standards |
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| Patterns, Functions and Algebra Standard |  |
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| Benchmarks (8 - 10) |
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| C. | Translate information from one representation (words, table, graph or equation) to another representation of a relation or function. |
| D. | Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations. |
| G. | Solve quadratic equations with real roots by graphing, formula and factoring. |
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| Grade Level Indicators (Grade 8) |
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| 1. | Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form. |
| 7. | Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. |
| 8. | Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems. |
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| Grade Level Indicators (Grade 9) |
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| 2. | Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations. |
| 3. | Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations. |
| 10. | Solve quadratic equations with real roots by factoring, graphing, using the quadratic formula and with technology. |
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| Grade Level Indicators (Grade 10) |
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| 10. | Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions. |
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| Principles and Standards for School Mathematics |
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| Algebra Standard |  |
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| Understand patterns, relations, and functions |
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| Expectations (9 - 12) |
| understand relations and functions and select, convert flexibly among, and use various representations for them; |
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| RESOURCE TYPE |
| Rich Problem, Inquiry, or Exploration |
| STANDARDS ALIGNMENT |
| 8 - 12 |
| TOPICS |
Mathematics -- Algebra; Nonlinear functions; Quadratic equations; Representation |
| KEYWORDS |
| quadratic functions |
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Author: Teresa Graham Publisher: Ohio Resource Center
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