It’s Neither Linear Nor Exponential
• Model a context with a quadratic function and interpret values of the function in context. • Graph a quadratic function and interpret the graph. • Find the average rate of change over a unit interval and compare rates for successive intervals.
This hook lesson touches on topics that arise throughout the unit: modeling with quadratic functions, interpreting their graphs in terms of a context, the way quadratic functions grow, and solving quadratic equations. The specific quadratic function used is of the simplest type and students do not have to carry out extensive manipulations. Rather, the context provides a motivation for learning those manipulations.
WHAT: In the musical Les Miserables, Inspector Javert holds his last note for eight seconds as he jumps off a bridge in Paris. Students are given data and develop an equation for distance fallen as a function of time F-BF.A.1a, A-CED.A.2. They graph this function to estimate out how high the bridge would have to be, and for how long he should actually hold the note, given the height of typical Paris bridges MP.4, F-IF.C.7a. Then students investigate the distance traveled over each one-second interval and discover that Javert’s velocity changes linearly F-IF.B.6 MP.8.
WHY: The context introduces students to quadratic functions in an engaging way. There is a natural desire to construct the function because comparing the length of the note with experience suggests the bridge is unrealistically high, so we want to use the length of the note to find the height.
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