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A-Rei Springboard Dive
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The problem presents a context where a quadratic function arises. Careful analysis, including graphing, of the function is closely related to the context. The student will gain valuable experience applying the quadratic formula and the exercise also gives a possible implementation of completing the square.

Author:
Illustrative Mathematics
Algae Blooms
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The problem statement describes a changing algae population as reported by the Maryland Department of Natural Resources. In part (a), students are expected to build an exponential function modeling algae concentration from the description given of the relationship between concentrations in cells/ml and days of rapid growth (F-LE.2).

Author:
Illustrative Mathematics
Algebra: Functions Part 3
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This lesson concludes the demonstrations of function exercises and introduces the graph as a definition of a function.

Author:
Khan, Salman
Algebra: Functions Part 4
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This is an example of a function problem that was submitted bya YouTube viewer.

Author:
Khan, Salman
Average Cost
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In this real world problem students solve questions based on the relationship between production costs and price.

Author:
Illustrative Mathematics
Bacteria Populations
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This task provides a real world context for interpreting and solving exponential equations. There are two solutions provided for part (a). The first solution demonstrates how to deduce the conclusion by thinking in terms of the functions and their rates of change. The second approach illustrates a rigorous algebraic demonstration that the two populations can never be equal.

Author:
Illustrative Mathematics
Baseball Cards
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This task could be put to good use in an instructional sequence designed to develop knowledge related to students' understanding of linear functions in contexts. Though students could work independently on the task, collaboration with peers is more likely to result in the exploration of a range of interpretations.

Author:
Illustrative Mathematics
Basketball Rebounds
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This task involves a fairly straightforward decaying exponential. Filling out the table and developing the general formula is complicated only by the need to work with a fraction that requires decisions about rounding and precision.

Author:
Illustrative Mathematics
Battery Charging
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This task describes two linear functions using two different representations. To draw conclusions about the quantities, students have to find a common way of describing them. We have presented three solutions (1) Finding equations for both functions. (2) Using tables of values. (3) Using graphs.

Author:
Illustrative Mathematics
Bike Race
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The purpose of this task is for students to interpret two distance-time graphs in terms of the context of a bicycle race. There are two major mathematical aspects to this: interpreting what a particular point on the graph means in terms of the context, and understanding that the "steepness" of the graph tells us something about how fast the bicyclists are moving.

Author:
Illustrative Mathematics
Braking Distance
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This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.

Author:
Illustrative Mathematics
Building a General Quadratic Function
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This task is for instructional purposes only and builds on ``Building an explicit quadratic function.''

Author:
Illustrative Mathematics