ALEX Classroom Resources

   View Standards     Standard(s): [MA2019] REG-8 (8) 13 :

13. Determine whether a relation is a function, defining a function as a rule that assigns to each input (independent value) exactly one output (dependent value), and given a graph, table, mapping, or set of ordered pairs.

[MA2019] ACC-8 (8) 33 :

33. Use the mathematical modeling cycle to solve real-world problems involving linear, quadratic, exponential, absolute value, and linear piecewise functions. [Algebra I with Probability, 31]

[MA2019] AL1-19 (9-12) 31 :

31. Use the mathematical modeling cycle to solve real-world problems involving linear, quadratic, exponential, absolute value, and linear piecewise functions.

In this video lesson, students use linear functions to model real-world situations. Students are given data for an almost linear relationship and develop a linear model. They use their model to make predictions and discuss the reasonableness of the model. Sometimes it is difficult to tell from the information given if a linear model is appropriate. When none of the given data perfectly fit by a linear function, students have to determine whether a linear approximation is reasonable and for which values it would be reasonable. Students also use piecewise linear graphs to find information about the real-life situation they represent. In situations where a quantity changes at different constant rates over different time intervals, students model the situation with a piecewise linear function.

   View Standards     Standard(s): [MA2019] ACC-8 (8) 27 :

27. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). [Algebra I with Probability, 25]

[MA2019] ACC-8 (8) 30 :

30. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Note: Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; symmetries; and end behavior. Extend from relationships that can be represented by linear functions to quadratic, exponential, absolute value, and general piecewise functions. [Algebra I with Probability, 28]

[MA2019] ACC-8 (8) 33 :

33. Use the mathematical modeling cycle to solve real-world problems involving linear, quadratic, exponential, absolute value, and linear piecewise functions. [Algebra I with Probability, 31]

[MA2019] AL1-19 (9-12) 25 :

25. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

[MA2019] AL1-19 (9-12) 28 :

28. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Note: Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; symmetries; and end behavior. Extend from relationships that can be represented by linear functions to quadratic, exponential, absolute value, and linear piecewise functions.

[MA2019] AL1-19 (9-12) 31 :

31. Use the mathematical modeling cycle to solve real-world problems involving linear, quadratic, exponential, absolute value, and linear piecewise functions.

[MA2019] MOD-19 (9-12) 9 :

9. Use the Mathematical Modeling Cycle to solve real-world problems involving the design of three-dimensional objects.

[MA2019] AL2-19 (9-12) 22 :

22. Use the mathematical modeling cycle to solve real-world problems involving polynomial, trigonometric (sine and cosine), logarithmic, radical, and general piecewise functions, from the simplification of the problem through the solving of the simplified problem, the interpretation of its solution, and the checking of the solution's feasibility.

Previously in this video series, students used simple quadratic functions to describe how an object falls over time given the effect of gravity. In this video lesson, they build on that understanding and construct quadratic functions to represent projectile motions. Along the way, they learn about the zeros of a function and the vertex of a graph. They also begin to consider appropriate domains for a function given the situation it represents.

Students use a linear model to describe the height of an object that is launched directly upward at a constant speed. Because of the influence of gravity, however, the object will not continue to travel at a constant rate (eventually it will stop going higher and will start falling), so the model will have to be adjusted (MP4). They notice that this phenomenon can be represented with a quadratic function and that adding a squared term to the linear term seems to “bend” the graph and change its direction.